After dropping out of the race against Utah Sen. Robert F. Bennett , state Attorney General Mark Shurtleffsays he’s looking for another way to help defeat the three-term senator in next year’s Republican primary.

Shurtleff, as a statewide office-holder already, had been considered an attractive prospect for conservatives eager to be represented by someone less likely to compromise with the Democrats who run Congress.

In an interview, Shurtleff said he has spoken with two potential “bigger name” GOP candidates, and he will consider throwing his support behind one of them.

Among the names that have been floated since Shurtleff dropped his bid earlier this week are businessman Fred Lampropoulos, a former gubernatorial candidate who has deep pockets and statewide GOP connections, and Mike Lee, a former gubernatorial general counsel and the son of former U.S. Solicitor General Rex Lee.

Rep. Jason Chaffetz , R-Utah, has made no moves to indicate he is serious about the race, but told the Salt Lake Tribune this week that he has not ruled out a Senate run.

Shurtleff expressed doubt that any of the three remaining GOP challengers in the race would be able to mount a serious challenge to Bennett next year. They are business owner Cherilyn Eager, businessman James Williams and entrepreneur Tim Bridgewater.

“Without taking anything away from the current candidates who are still in there against Sen. Bennett I don’t think they can win,” Shurtleff said.

Bennett isn’t waiting to gauge the strength of his rivals and would-be rivals from the right; the Deseret News reported Friday that the senator was airing an advertisment showcasing his opposition to President Obama’s health care overhaul.

Bank Bailout Fallout

The moves to challenge Bennett in the primary can be traced back to his efforts to help pass the Troubled Asset Relief Program in 2008. While he was hailed on Capitol Hill as a chief negotiator on the bill, that distinction has turned into a dubious one back home in Utah, which remains one of the most conservative states in the country.

That bit of legislating also put Bennett in the crosshairs of the anti-tax group Club for Growth, which has made him an early target this cycle.

Under Utah’s party convention format, a candidate can avoid a primary by earning 60 percent of the delegate vote at a nominating convention in May. If that doesn’t happen, the top two finishers face off in a June primary.

Bennett raised just over $400,000 in the third quarter and reported $792,000 in cash on hand as of Sept. 30. Shurtleff raised just over $100,000 in the same time period and reported $146,000 in the bank at the end of the third quarter.