WASHINGTON — When President Obama nominates Chuck Hagel, the maverick Republican and former senator from Nebraska, to be his next secretary of defense, he will be turning to a trusted ally whose willingness to defy party loyalty and conventional wisdom won his admiration both in the Senate and on a 2008 tour of war zones in Iraq and Afghanistan.

The choice of Mr. Hagel, the first Vietnam veteran to be nominated for the post, would add a prominent Republican to Mr. Obama’s cabinet, providing some political cover for the president’s plans to exit Afghanistan and make cuts to a military budget that has roughly doubled since the 2001 terrorist attacks.

But Republicans made clear on Sunday that they would give Mr. Hagel a rough ride on his path to the Pentagon, questioning his support for Israel, his seriousness about the Iranian nuclear threat and his commitment to an adequate defense budget. And Mr. Obama may also face difficulties from some Democrats who are wary of negative comments that Mr. Hagel made more than a decade ago about gays.

Some Obama aides had doubts about the wisdom of the choice, given Mr. Hagel’s frosty relationship with members of his own party, but officials said they were confident that they could corral enough votes from both sides of the aisle to win confirmation in the Senate. White House officials confirmed on Sunday that Mr. Hagel was Mr. Obama’s pick for the job and said the announcement would come as early as Monday.