Representative Liz Cheney of Wyoming, the No. 3 House Republican, announced on Tuesday that she would vote to impeach President Trump, saying there had “never been a greater betrayal by a president of the United States” than Mr. Trump’s incitement of a mob that attacked the Capitol last week.
In a stinging statement that drove a fissure through her party, Ms. Cheney dismissed fellow Republicans arguing that the impeachment was rushed, premature or unwarranted. Her words were unequivocal and likely to give cover to two dozen or so other House Republicans looking to break ranks and join an effort that was also said to have the tacit support of Senator Mitch McConnell of Kentucky, the Republican leader.
“Much more will become clear in coming days and weeks, but what we know now is enough,” said Ms. Cheney, the scion of a storied Republican political family. “The president of the United States summoned this mob, assembled the mob and lit the flame of this attack. Everything that followed was his doing. None of this would have happened without the president.”
She added: “The president could have immediately and forcefully intervened to stop the violence. He did not.”
[Here is a list of Republicans supporting Trump’s impeachment.]
Ms. Cheney’s announcement came a short time after Representative John Katko of New York became the first House Republican to commit to voting to impeach.
“To allow the president of the United States to incite this attack without consequence is a direct threat to the future of our democracy,” Mr. Katko said in a statement to Syracuse.com. “For that reason, I cannot sit by without taking action. I will vote to impeach this president.”
Representatives Adam Kinzinger of Illinois and Fred Upton of Michigan, both Republicans, followed them.
If Mr. Trump’s actions “are not worthy of impeachment, then what is an impeachable offense?” Mr. Kinzinger said in a statement.
House Republican leaders have decided not to formally lobby members of the party against voting to impeach Mr. Trump, making an implicit break with him as they scrambled to gauge support within their ranks for a vote on Wednesday to charge him with inciting violence against the country.
Not a single Republican voted in favor of impeachment during the 2019 proceedings.
This time, Mr. Trump’s encouragement of the mob “cannot be ignored,” said Mr. Katko, a moderate who represents a district in upstate New York that voted for President-elect Joseph R. Biden Jr.
“By deliberately promoting baseless theories suggesting the election was somehow stolen, the president created a combustible environment of misinformation, disenfranchisement and division,” Mr. Katko said. “When this manifested in violent acts on Jan. 6, he refused to promptly and forcefully call it off, putting countless lives in danger.”
Mr. McConnell of Kentucky has told associates that he believes Mr. Trump committed impeachable offenses and that he approves of the House moving forward with the Constitution’s most severe punishment.
If the impeachment charge were to result in a Senate conviction, the Senate could vote to bar the president from holding public office again. Two Senate Republicans had already called on Mr. Trump to resign, and advisers privately speculated that an additional dozen or so could ultimately favor convicting him at trial.
If all senators were voting, 17 Republicans would have to join Democrats to convict Mr. Trump of high crimes and misdemeanors; if they did so, only a majority would be required to disqualify him from being elected again.
Among the other House Republicans who were said to be considering voting to impeach were stalwart moderates from swing districts, like Representative Jaime Herrera Beutler of Washington, as well as newly seated freshmen, like Peter Meijer of Michigan.