The draft, citing "incitement of insurrection," could be introduced Monday.
President Donald Trump is slated to hand over control of the White House to President-elect Joe Biden in 11 days.
Sen. Chuck Grassley interrupted the proceedings, taking over for Vice President Mike Pence to preside over the Senate -- calling the Senate into recess subject to the call of the chair as protesters breached the inside of the U.S. Capitol building.
Pence appeared to have been moved out of the Senate chamber. The House of Representatives was being evacuated.
As protesters of the Electoral College count and supporters of the president breached the Capitol building, Trump did not call for calm but attacked Vice President Mike Pence on Twitter.
"Mike Pence didn’t have the courage to do what should have been done to protect our Country and our Constitution, giving States a chance to certify a corrected set of facts, not the fraudulent or inaccurate ones which they were asked to previously certify. USA demands the truth!" Trump tweeted.
Trump supporters were seen scaling the Capitol building steps as the proceedings continued inside. Some breached security to make it inside, to near the Senate chamber.
Senate Minority Leader Chuck Schumer lectured lawmakers in the chamber, saying an element of the GOP "believes their political viability hinges on the endorsement of an attempted coup."
"By the end of the proceedings today it will be confirmed once again something that is well-known and well-settled: the American people elected Joe Biden and Kamala Harris to be the next president and vice president of the United States," Schumer said.
Schumer said Republicans know this fact but will object to the counting of the vote anyway -- "and in the process they will embarrass themselves, they will embarrass their party, and worst of all they will embarrass their country."
"As we speak, half of our voters are being conditioned by the outgoing president to believe that when his party loses an election, the results must not be legitimate. As we speak the eyes of the world are on this chamber questioning whether America’s still the shining example of democracy, the shining city on the hills. What message we send today, what message will we send today to our people, to the world that has so looked up to us for centuries?”
As Schumer spoke, protesters breached the perimeter outside the U.S. Capitol Building and the building went on lockdown.
A notice from United States Capitol Police to all buildings within the Capitol Complex said, "Due to an external security threat located on the West Front of the U.S. Capitol Building, no entry or exit is permitted at this time. You may move throughout the building(s) but stay away from exterior windows and doors. If you are outside, seek cover."
-ABC News' Mariam Khan, Allie Pecorin and Trish Turner
Kicking off up to two hours of debate on the Senate floor after some GOP lawmakers objected to the electoral vote count in Arizona, Senate Majority Leader Mitch McConnell made an extraordinary speech rebuking his fellow Republicans for their actions.
"We’re debating a step that has never been taken in American history – whether Congress should overrule the voters and overturn a presidential election."
Speaking directly to his colleagues, he reminded them he supported Trump's right to legal challenges, "But over and over, the courts rejected these claims including all-star judges whom the president himself has nominated."
"We cannot simply declare ourselves a national board of elections on steroids. The voters, the courts, and the states have all spoken,” he said. “If we overrule them, it would damage our republic forever."
“This election is not unusually close,” he added.
McConnell went on to say overturning the results would send the country on a "poisonous path” and into an "endless spiral of partisan vengeance” before calling on elected leaders to summon "patriotic courage" in both victory and in defeat.
"We must not imitate and escalate what we repudiate," he said.
"I will not pretend such a vote would be a harmless protest gesture while relying on others to do the right thing. I will vote to respect the people's decision and defend our system of government as we know it," McConnell said in closing.
-ABC News' Trish Turner
