“We need to accept our institutions. They worked in 2016,” Mr. Cole said in an interview. “They worked again in 2020.”
Elected officials, he said, need to “be honest with your voters.”
“You have to recognize when you are not successful, and you move on and accept the election results,” he said. “The American people, I hope, will do that.”
In the Senate, at least, that view appeared to be gaining currency.
In a statement, Senator Mike Lee, Republican of Utah and a defender of the president, said that “absent new information that could give rise to a judicial or legislative determination altering the impact of today’s Electoral College votes, Joe Biden will become president of the United States.” An aide said he had no plans to join Mr. Brooks in challenging the results.
Another leading contender for that task, Senator Ron Johnson, Republican of Wisconsin, seemingly threw cold water on the idea as well. Though Mr. Johnson plans to convene a hearing on Wednesday to give Mr. Trump’s specious arguments of voting fraud an airing in Congress, he told the Milwaukee Journal Sentinel that he thought the outcome was legitimate and he did not plan to object to the Electoral College results.
Still, other possible contenders remained. One was Tommy Tuberville, the newly elected Alabama Republican. Another possible candidate, those watching the process said, was Senator Kelly Loeffler of Georgia, one of the two Republicans competing in January runoffs that will determine which party controls the Senate next year. Those races will play out the day before the joint session to ratify the presidential election results convenes in Washington.
Ms. Loeffler’s office did not respond to a question about Mr. Biden on Tuesday, but on Twitter, she suggested she was not ready to accept the result.
“I will never stop fighting for @realDonaldTrump because he has never stopped fighting for us!” she wrote.
Luke Broadwater and Emily Cochrane contributed reporting.