HOMEWOOD, Ala. — Senator Luther Strange of Alabama wields an endorsement from the president of the United States, is the beneficiary of a multimillion-dollar campaign from allies of Mitch McConnell, the Senate majority leader, and has the backing of influential conservative interest groups like the National Rifle Association.

But Mr. Strange is wheezing into Tuesday’s Republican Senate primary here. He is grasping to secure a second-place finish and a slot in a September runoff with Roy S. Moore, the twice-deposed former State Supreme Court justice and evangelical-voter favorite who is expected to be the top vote-getter but may fall short of the majority needed to win outright.

Mr. Strange is in a political vise, pinched by his links to a pair of Republicans, one local and one national, held in low esteem by many in the party here: the disgraced former Gov. Robert Bentley, who appointed Mr. Strange, and Mr. McConnell.

The senator’s difficulties owe chiefly to how he found his way to fill the seat vacated by Attorney General Jeff Sessions, a story rooted in the sex scandal of Mr. Bentley. Yet Mr. Strange, who is 6-foot-9 and known to many as “Big Luther,” is also bumping into the enduring contempt grass-roots conservatives harbor toward the party establishment, an animus now principally directed toward Mr. McConnell.