Senator Thom Tillis of North Carolina, a Republican who rode Mr. Trump’s coattails to re-election last month, called Mr. Biden the “presumptive president,” pending the outcome of any lawsuits yet unresolved.
Others were more direct.
“We’ll deal with Vice President Biden as the president-elect,” said Senator Roy Blunt of Missouri, the chairman of the Republican Policy Committee and the congressional panel planning next year’s inauguration. Just last week, Mr. Blunt voted against a resolution by Democrats that would have forced the inaugural planning committee to acknowledge Mr. Biden’s victory.
“We’ve now gone through the constitutional process,” he said Monday.
After initially dismissing a query about the Electoral College results as a “gotcha question,” Senator John Barrasso of Wyoming, the third-ranking Republican leader, said he would “respect the result of the Electoral College vote today” even if he was disappointed.
Still, many of Mr. Trump’s most ardent backers did not appear ready to change course.
Senator Ron Johnson, Republican of Wisconsin, planned to convene a hearing on Wednesday to give Mr. Trump’s claims an airing in the halls of Congress.
That posture has infuriated Democrats and even some Republicans, who warned again on Monday that by pressing Mr. Trump’s false claims about the election, the party was willfully misleading voters and abetting a threat to the democratic process itself.
“It is unacceptable for political candidates to treat our election system as though we are a third-world nation and incite distrust of something so basic as the sanctity of our vote,” Representative Paul Mitchell of Michigan wrote in a letter to Ronna McDaniel, the Republican National Committee chairwoman, and Representative Kevin McCarthy of California, the party’s top House leader.
Mr. Mitchell, a member of his party’s leadership who is retiring, released the letter shortly after his state cast its 16 electoral votes for Mr. Biden. He wrote that he was leaving the Republican Party over its refusal to accept Mr. Trump’s defeat, and warned that his colleagues were risking “long-term harm to our democracy.”