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In Iowa, the GOP is on the lookout for someone to run against Rep. Bruce L. Braley, the likely Democratic nominee, now that GOP Reps. Tom Latham and Steve King have balked at running for retiring Democratic Sen. Tom Harkin’s seat.

The headaches continue in Colorado, where the GOP remains without a challenger to Sen. Mark Udall after Rep. Cory Gardner announced this week that he would not run against the vulnerable Democrat.

Louisiana is more complicated.

The GOP appears to be clearing a path for Rep. Cassidy to take on incumbent Democrat Mary L. Landrieu — but there are still questions about how the Baton Rouge congressman would do in a statewide race. “At this point, he looks like a ‘generic Republican,’ which might very well be enough,” Mr. Kondik said.

Then there are the seats where the GOP must play defense — including the open seat in Nebraska, where Mr. Johanns is retiring.

Former Nebraska state treasurer Shane Osborn has expressed interest in running. Mr. Sasse, who is president of Midland University but has never held elected office, moved closer to running this week when he announced that he would be taking part in a 45-day listening tour of Nebraska.

Pointing to his 2007 to 2009 stint as assistant secretary of Health and Human Services, Mr. Sasse said he wants to stop the “devastating impact Obamacare implementation will have on Nebraska families and small businesses.”

“I will tell you that there is no way this monstrosity can be implemented,” he said.

Mark A. Fahleson, who recently stepped down as Nebraska GOP chairman, praised Mr. Sasse, calling him “Nebraska’s Jack Kemp.”

Ben is a cultural and economic conservative who has the intellect to be able to articulate a message that is optimistic,” Mr. Fahleson said. “He has the ability to talk about entrepreneurial capitalism, but he also has the ability to talk to people here in Nebraska who differ from him ideologically, but who come away saying, ‘Even though I don’t agree with him on every issue, he is the guy I want representing us in the U.S. Senate.’”

The door opened for Mr. Sasse after Gov. Dave Heinman and Rep. Jeff Fortenberry announced they would not run.

“Nebraska does have a history of people coming from outside of the established political offices to secure statewide position — I am thinking of Chuck Hagel and Bob Kerrey — so it will be interesting to see if the Sasse thing develops,” said John Hibbing, a political-science professor at the University of Nebraska-Lincoln. “Those who know him seem impressed, but he is largely unknown so there are many opportunities for his candidacy to crash and burn.”