U.S. Senate candidate, Thom Tillis, left, holds 4-month-old Charlie Smith for a photo beside his wife, Susan Tillis, while campaigning at the Morrison Regional Library as voters come to vote on Saturday, May 3, 2014. Credit: Charlotte Observer

Mitt Romney threw his support behind Republican Thom Tillis's bid for U.S. Senate in North Carolina a day ahead of a crucial primary election in which Tillis appears to be on the cusp of winning enough votes to avert a runoff.

"I am proud to support Thom Tillis for US Senate. Now more than ever, Americans need problem-solvers in Washington, DC. Thom is a conservative who has been solving problems in North Carolina as Speaker of the House and I am confident he will do the same in Washington," Romney said in a statement Monday.

Romney's endorsement comes as Tillis, the state House speaker and choice of the Republican establishment, is trying to fend of challenges from lesser-known Republicans running to his right. On Monday, one of those challengers, tea party-aligned obstetrician Greg Brannon, will campaign Monday afternoon with Sen. Rand Paul (R-Ky.).

Tillis must clear 40 percent of the vote in Tuesday's GOP primary to avert a runoff election, which would mean expending more resources ahead of a likely matchup against Sen. Kay Hagan (D). Polls show him hovering around 40 percent.