(CNN) -- House Speaker Nancy Pelosi announced Wednesday that Congress would resume the certification of the Electoral College votes on Wednesday after rioters incited by President Donald Trump breached the Capitol and halted the process of declaring President-elect Joe Biden the winner of the 2020 election.

Pelosi said that following calls with the Pentagon, Justice Department and Vice President Mike Pence, the count would resume at the Capitol once it was cleared for use.

Lawmakers in both parties made clear they were determined to finish the count following the chaos at the US Capitol on Wednesday when the House and Senate debates on an objection to Arizona's election results were halted by the rioters surrounding the chambers.

**This image is for use with this specific article only**

Congressional Republicans are preparing a futile attempt on President Donald Trump's behalf to overturn the results of the November election by objecting to Electoral College votes cast by at least three states for President-elect Joe Biden. Seen here, the Capitol at dawn in Washington D.C., on January 4, 2021.

As senators wait to get back on the Senate floor and resume the certification process, some senators are using the time -- and the scary reality of what is happening -- to push and cajole the GOP senators who planned to object to states like Georgia and Pennsylvania to back down after they finish debate over Arizona's election results, two Senate sources familiar with the conversations tell CNN.

"We're trying to expedite matters," said Sen. Roger Wicker, a Mississippi Republican, predicting the counting would be finished Wednesday evening.

West Virginia Democratic Sen. Joe Manchin, leaving a secure location with other senators, said there's a belief they will finish the electoral vote count Wednesday night.

"These thugs aren't running us off," Manchin said.

House Majority Whip Jim Clyburn tweeted that the certification would continue Wednesday evening. "This authoritarian menace will not succeed in his attempts to overthrow our democratically elected government," the South Carolina Democrat said.

It's not yet clear whether the senators planning to object, including Missouri GOP Sen. Josh Hawley, will drop those objections.

The main Senate objectors were privately meeting Wednesday evening to strategize about whether they plan to press ahead with their objections. The discussions come as leaders are planning to continue with the House and Senate session sometime Wednesday evening, but pressure is building on the senators to limit their objections and show unity after the raucous and violent display in the Capitol.

Sens. Mike Braun of Indiana, Ted Cruz of Texas, Hawley and a few others were seen meeting in a separate room together outside of the bigger room where all senators are being held.

When Braun was asked by reporters if they've reached any resolution, he replied, "Not yet."

The House and Senate had just started debating a Republican objection to Arizona's election results Wednesday afternoon when the rioters breached the barrier outside the Capitol and soon thereafter, the Capitol itself. Both the House and Senate recessed their sessions in response to the scene unfolding outside: Capitol Police drew their guns at a barricaded House door as lawmakers evacuated the chamber.

The dangerous and unprecedented scene at the Capitol threw the process of counting the Electoral College votes into disarray, prompting the evacuation of Vice President Mike Pence and House and Senate leaders as the rioters stormed into the building.

A source told CNN that GOP Rep. Liz Cheney and Democratic Rep. Hakeem Jeffries, the leaders of their respective conferences, told members -- together -- that the National Guard was on the way and they would return to the floor as soon as they could. The violence, they said, would not keep them from doing their job. The whole room applauded, the source said.

Jeffries told reporters: "The Capitol is being cleared. When it is safe, we will return to complete our Constitutional responsibilities. This is the United States. We will not allow mob rule to undermine the rule of law."

Republicans and Democrats alike condemned the protesters for breaching the US Capitol, and several blamed Trump -- who pushed for Republicans and Pence to use the joint session of Congress to overturn the election result -- for the dangerous situation that unfolded.

"You are not protecting the country. Where is the DC guard? You are done and your legacy will be a disaster," tweeted Illinois GOP Rep. Adam Kinzinger.

Speaking in Delaware, Biden called on Trump to demand an "end to this siege."

"Our democracy is under unprecedented assault, unlike anything we've seen in modern times, an assault in a citadel of liberty: The Capitol itself," he said.

Trump subsequently urged protesters in a video to "go home" while repeating his unfounded claims about a stolen election.

"You have to go home now. We have to have peace," Trump said. "We have to have law and order."

The Electoral Count Act, the 19th century law governing Wednesday's proceedings, does not require Congress to finish counting on January 6.

Before the chaos, McConnell rebuked Trump

The chaos broke out after Senate Majority Leader Mitch McConnell on Wednesday delivered a forceful rebuke of Trump's baseless claims of widespread election fraud, warning his fellow Republicans of the damage their efforts to try to overturn the election won by Biden could do to democracy.

"The Constitution gives us here in Congress a limited role. We cannot simply declare ourselves the national board of elections on steroids," McConnell said on the Senate floor. "The voters, the courts and the states have all spoken. They've all spoken. If we overrule them, it would damage our Republic forever."

McConnell had opened the Senate's debate of an objection to Arizona's election results that was formally lodged by a group of House and Senate Republicans.

The push is destined to fail, with Democrats and a significant number of Republicans planning to vote down all of the objections in both the House and the Senate, criticizing the effort both as a hopeless attempt to reverse the election outcome and as a threat to democracy that would subvert the will of the voters.

Track the electoral vote count in Congress

The question now is whether Republicans will still try to push their objections in the wake of the rioting at the Capitol.

Sen. Rand Paul, a Kentucky Republican, tweeted a thread in opposition to voting against the election results, describing it as "the speech I'll be giving today from an undisclosed location."

"The vote today is not a protest; the vote today is literally to overturn the election! Voting to overturn state-certified elections would be the opposite of what states' rights Republicans have always advocated for," Paul said.

During the brief Senate debate, Cruz, who joined the House Republicans' objection of Arizona's results, pointed to polling that has shown millions of Americans believe the election was rigged -- polling that has been fueled by Trump's repeated false claims about the election outcome.

Cruz argued that he isn't calling for "setting aside the results of the election" -- even though Trump plainly is -- but Cruz pushed instead for an electoral commission to investigate claims of voter fraud. Democrats and many of Cruz's fellow Republicans, however, have argued there's no role for Congress to interfere in state elections.

While there is no evidence of widespread voter fraud, Trump and his campaign have been pushing baseless and false conspiracy theories that the election was rigged against him. The President and his allies lost dozens of lawsuits across the country both claiming fraud and challenging the constitutionality of state election laws altered due to the Covid-19 pandemic.

All eyes on Pence

As his losses have mounted, Trump has gone after the courts that ruled against him, state election officials and lawmakers who haven't embraced his conspiracy theories or tried to overturn the will of the voters, Senate Republicans who oppose his anti-democratic push to overturn the Electoral College result and even Pence, who presided over Wednesday's joint session of Congress before he was evacuated.

Trump addressed his supporters who converged on Washington near the White House on Wednesday morning, continuing to pressure Pence to go beyond his authority in Wednesday's joint session of Congress.

"I hope Mike is going to do the right thing," Trump said at the rally on the Ellipse. "If Mike Pence does the right thing, we win the election."

But Pence wrote in a letter to lawmakers Wednesday that he did not have the "unilateral authority" to intervene.

"Our Founders were deeply skeptical of concentrations of power and created a Republic based on separation of powers and checks and balances under the Constitution of the United States," Pence wrote. "Vesting the Vice President with unilateral authority to decide presidential contests would be entirely antithetical to that design."

Congress' counting of the Electoral College votes is typically little more than an afterthought, after the Electoral College officially votes for President in December. Just twice since the process was established in the 19th century have votes been forced on Electoral College results, and several other would-be challenges have quickly fizzled because no senator joined them.

McConnell sought to dissuade any senators from signing onto the objections to the Electoral College votes, which would have prevented roll-call votes on the challenges. But last week, Missouri GOP Sen. Josh Hawley announced he would join the objection to Pennsylvania.

Rep. Paul Gosar, an Arizona Republican, objected to Arizona's election results, along with with Sen. Ted Cruz of Texas.

Georgia GOP Sen. Kelly Loeffler -- who CNN projects has lost her seat to Democrat Raphael Warnock but will remain in office until Tuesday's Georgia runoff results are certified -- has signaled she will object to Georgia's result. It's not clear if she still plans to do so.

Joint session in the shadow of Georgia's runoff

Wednesday's events played out as Democrats swept the Georgia Senate races, taking control of a 50-50 Senate after Biden is sworn in and Vice President-elect Kamala Harris becomes the Senate's tie-breaking vote.

The question of how to handle the count had created a major divide inside the Republican Party. The Senate Republican fight spilled into the open last week following Hawley's announcement, with Trump attacking McConnell and other Republicans who haven't joined.

In the House, No. 3 Republican Cheney -- daughter of former Vice President Dick Cheney -- has forcefully pushed back on the objections, while Minority Leader Kevin McCarthy has quietly backed them.

For every state where there's a House member and senator objecting, the two chambers separate and debate for two hours, before voting on the objection. Aides had predicted each state objection will take as much as four hours.

The states' votes are read alphabetically. If either chamber votes down the objection after the debate, the states' votes are counted and then counting continues.

The last time a lawmaker forced votes on the Electoral College results was in 2005, when Sen. Barbara Boxer, a California Democrat, objected to President George W. Bush's win in Ohio, which she said was never an effort to overturn the election result. In 2017, a group of House Democrats raised several objections to states Trump won, but they were gaveled down because they didn't have a senator join -- by then-vice president Biden.