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Soon after winning the nomination, though, Mr. Akin claimed that women’s bodies have ways of rejecting pregnancies from “legitimate rape” — a remark that led to problems for the GOP nationwide. Indeed, it was a follow-up to Mr. Akin’s comment that caused Mr. Mourdock’s own falter.

Republican leaders urged Mr. Akin to drop out of the race to allow the party to name a replacement, but he refused, and has trailed Mrs. McCaskill in the polls ever since.

The GOP was also hit by some difficult retirements, including Sen. Olympia J. Snowe in Maine, whose decision opened the way for independent former Gov. Angus King to run. Polls show him poised to defeat both the Republican and Democratic nominees there, and both sides expect him to caucus with Democrats.

The only races that are safe for Republicans this year are in the reddest of red states: Texas, Mississippi, Tennessee, Wyoming and Utah.

Meanwhile, in Montana, North Dakota and Arizona, where Mitt Romney is poised to top President Obama in the presidential balloting, Democratic Senate candidates are competitive. And in West Virginia, where Mr. Romney will steamroll, Democratic Sen. Joe Manchin III is poised for an easy re-election.