"Let's give President-elect Biden the 100 days" at the start of his term to deal with the most urgent issues, Democratic House whip James Clyburn told CNN.
Ms Murkowski, who has long voiced her exasperation with Mr Trump's conduct in office, said on Friday that Mr Trump simply "needs to get out".
The five dead included one Capitol Police officer, beaten as he tried to ward off the crowds.
Sen. Patrick Toomey, R-Pa., on Sunday joined Sen.
Corporate America began to show its reaction to the Capitol riots by tying them to campaign contributions.
The two men have not spoken since Wednesday when Pence informed Trump that he would not be going along with Trump's unconstitutional scheme to throw out legal electoral voters in his bid to overturn the election.
Mr Toomey said that resignation was the "best path forward, the best way to get this person in the rear view mirror for us".
House leaders, furious after the insurrection, appear determined to act against Trump despite the short timeline.
And Senator Joe Manchin of West Virginia, a centrist Democrat whose vote could be crucial in the new, evenly divided Senate, told CNN an impeachment after January 20 "doesn't make any common sense whatsoever". "As the days go by, the horror of the ongoing assault on our democracy perpetrated by this President is intensified and so s the immediate need for action". "There must be a recognition that this desecration was instigated by the President".
A new ABC News/Ipsos poll released Sunday found that over half of Americans - 56% - believe that Trump should be removed from office before his term ends.
In an interview aired Sunday on CBS's "60 Minutes", Pelosi said, "I like the 25th Amendment, because it gets rid of him".
- The New York Times called the impeachment process "deliberately difficult" where the House first votes on impeachment and if there is a simple majority, the Senate will have to "consider them at a trial".
Proceedings would then move to the Senate, where a two-thirds vote is necessary for a president's removal.
Late Saturday, House Speaker Nancy Pelosi, D-Calif., sent a letter to her colleagues reiterating that Trump must be held accountable. "And he had a huge part, a huge role to play in that", Hogan said.
Several prominent US corporations, including Marriott International Inc and JPMorgan Chase & Co, have said they will suspend donations to the almost 150 Republicans who voted against certifying Biden's victory, and more are considering that step. He once referred to it publicly - and in front of Pompeo and reporters - as "the deep State Department", a reference to what Trump and his supporters believe is a cabal of entrenched bureaucrats intent on subverting his policies.
Nebraska Sen. Ben Sasse said he would take a look at any articles that the House sent over.
Lisa Murkowski on Friday became the first Republican U.S. senator to say Trump should resign immediately.
Pro-Trump lawyer Lin Wood made death threats against Vice President Mike Pence last week, something that is now being investigated by the US Secret Service, Fox News has cited an unnamed law enforcement agency source as saying.
A growing number of GOP senators are urging President Donald Trump to resign or be impeached following the violent insurrection at the U.S. Capitol on Wednesday.
Potentially complicating Pelosi's decision about impeachment was what it meant for Biden and the beginning of his presidency.
Trump could face a historic second impeachment before the Jan 20 inauguration of Democrat Joe Biden, at a time when the United States is hit by a surging pandemic, a flagging economy and searing division.
While people close to Trump said they would certainly prefer he not become the only president in the nation's history to be impeached a second time, Jason Miller, a close adviser, noted that Trump's popularity rose after his first impeachment trial.
Marriott International, the world's largest hotel company and the Blue Cross Blue Shield Association (BCBSA) said Sunday they will suspend donations to US lawmakers who voted last week against certifying President-elect Joe Biden's victory.
"I think there is also a possibility that there is criminal liability here".
Trump, who has without evidence challenged the validity of Biden's election victory, praised and egged on supporters before they laid siege to the Capitol, where lawmakers were certifying the Electoral College vote for Biden.
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