Authorities continued seeking Trump supporters who violently stormed the Capitol on Wednesday after the president's repeated false claims that he had lost to Biden due to fraud.
Toomey said on NBC's "Meet the Press", calling Trump's behaviour since the election "outrageous".
Toomey, appearing on Sunday television news shows, said he did not think there was time for impeachment with only 10 days left in Trump's term, and noted there did not appear to be consensus to use the Constitution's 25th Amendment to strip Trump of his powers.
Murkowski on Friday became the first Republican senator to call for Trump's resignation, saying he bears responsibility for the violence that ensued at the Capitol.
Capitol security has been stepped up, with a seven-foot-tall (about two meters) black metal fence erected around the historic building.
"I honestly don't think impeachment is the smart move because I think it victimizes Donald Trump again", Kinzinger said.
Clyburn said it will likely be Tuesday or Wednesday before the House takes such a vote and suggested that after it passed, Democrats may wait several months before sending the impeachment measure to the Senate, which would ensure that a Senate trial wouldn't distract from President-elect Joe Biden's early legislative priorities or prevent the Senate from swiftly confirming Biden's Cabinet nominees.
Trump, who claimed the election was rigged in favour of his Democratic opponent, and just recently witnessed Facebook and Twitter shutdown his accounts for allegedly inciting violence, will not be the first U.S. president to have skipped his successor's inauguration ceremony.
"And so. the vice president is welcome to come, we would be honored to have him there, and to move forward in the transition".
The president has so far resisted all talk of resignation, and is reportedly furious over recent events - including Pence's rejection of Trump's vocal pressure to somehow intervene in Congress's confirmation on Wednesday of Biden's election win.
She urged members to "be prepared to return to Washington this week".
Reports have emerged that Mike Pence will be present at President-elect Joe Biden's inauguration on January 20. Through late Sunday, 210 House members have cosponsored the impeachment measure, or almost a majority of the House.
"The best way for our country, Chuck, is for the president to resign and go away as soon as possible", Toomey said.
Democrats, for their part, expressed concern that a Senate trial would overshadow and hamper Biden's efforts to quickly lay out his agenda, starting with the fight against the coronavirus and the need to support the economy.
"Maybe we'll send the articles sometime after that".