Walsh, who lost to Rep.-elect Tammy Duckworth (D-Ill.) by a wide margin in his 2012 reelection bid, said during a weekend rally that it would be "kind of fun to run against" Sen. Dick DurbinRichard (Dick) Joseph DurbinSenate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill MORE (D-Ill.) in 2014. He later said he was joking about the run, but didn't rule out another run for Congress — or for governor.

"This Republican Party needs a Scott Walker to run for governor, and I haven't seen or heard that candidate," Walsh said, referring to the conservative Wisconsin governor.