Among all the victories for Senate Republicans, Ms. Collins’s stood out as the most remarkable. Facing an onslaught of liberal outrage over her 2018 vote to confirm Justice Brett M. Kavanaugh to the Supreme Court amid accusations of sexual assault, she trailed the Democrat, Sara Gideon, the speaker of the Maine House of Representatives, in the race’s closing weeks.
In the end, she proved she was one of the only senators in the country still able to significantly outrun the top of the ticket, winning her fifth term even as Mr. Trump lost badly in Maine to Mr. Biden.
Still, already eying a 2022 Senate election on more difficult turf for Republicans, Mr. McConnell suggested there were reasons for the party to worry, as well.
Speaking to reporters after his own commanding victory in Kentucky, he said Republicans had pressing work to do to win back the support of women and college-educated voters, as well as to bolster their fund-raising apparatus, which has trailed Democrats’ juggernaut, ActBlue.
“I am disturbed by the loss of support in the suburbs nationwide,” Mr. McConnell said.
Democrats still remained hopeful about the races in Georgia. The Rev. Dr. Raphael G. Warnock, a Democrat, was headed for a January runoff against Senator Kelly Loeffler, the appointed Republican, in a special election to replace Senator Johnny Isakson, who retired in late 2019 citing health problems. Jon Ossoff, 33, a documentary filmmaker, was in a tight race to unseat Mr. Perdue, which could also end up in a runoff if neither cleared the 50 percent threshold required under Georgia law to win outright.
Both parties had other outstanding targets, but they were considered stretches. For Republicans, the best option was Michigan, where John James, a Black Iraq war veteran who ran for the Senate unsuccessfully in 2018, was trying to unseat Senator Gary Peters. Democrats still believed they had an outside shot of defeating Senator Dan Sullivan in Alaska.
Catie Edmondson contributed reporting.