In a Republican presidential field where no top-tier candidate offers a flawless resume, the question facing GOP primary voters is whether they can find a diamond in the rough — a standard-bearer who embodies the party’s conservative backbone and can give President Obama a run for his money.

With former Massachusetts Gov. Mitt Romney, the nominal front-runner in a wide-open field, set to formally enter the race Thursday, all of the top candidates have significant deviations from Republican orthodoxy on their records, while the second-tier hopefuls have yet to prove they can raise funds and energize base voters enough to threaten Mr. Obama’s re-election hopes.

That could pose problems for Republicans, who feel Mr. Obama’s record on health care and federal spending should make him ripe for a serious challenge in 2012. GOP officials at the very least want a strong presidential showing to help them hang on to control of the House and win the three or four seats needed to gain control of the Senate.