WASHINGTON — The tea party movement’s best remaining hope in 2012 for picking off an incumbent Republican in the Senate has boiled down to one state, Indiana, where six-term Sen. Richard Lugar still faces a challenge from the right.

Polls show Lugar is vulnerable and his record, dotted with votes for the Troubled Asset Relief Program and other government spending, is ripe for conservative critique, despite decades as one of the Senate’s foreign policy experts. But the tea party candidate challenging him in the GOP primary, state treasurer Richard Mourdock, lacks Lugar’s heft and name recognition.

It looked for a time as if three longtime Senate moderates — Orrin Hatch of Utah, Olympia Snowe of Maine and Lugar — were in danger of being taken down by primary challenges from the right. But the upstart campaigns in Utah and Maine have fizzled as Hatch and Snowe made concerted efforts to woo right-wing voters in their states.

Hatch’s best-positioned challenger, Rep. Jason Chaffetz, decided against a run. Hatch still must survive Utah’s byzantine convention nominating process, but unlike his former Senate colleague, Bob Bennett, he hasn’t been caught off guard and has spent months building his tea party credentials.

A minor tea party candidate has announced a run against Snowe, but she has the support of Gov. Paul LePage, the state’s most prominent tea party supporter, and efforts to target her haven’t gotten off the ground.

That leaves Mourdock, who has been running for months with little attention, as the tea party’s best shot in the Senate.

He is millions of dollars behind Lugar in fundraising.

He only recently began to seal the support of national tea party groups and his message still hasn’t reached voters who are looking for an alternative to the incumbent.

Matt Barns, a Republican voter from Indianapolis, knows precious little about Mourdock, even though he is inclined to support him.

Ask him about Lugar, though, and Barns’ thoughts are clear.

“It’s time for him to be put to pasture,” Barns said.

Gary Meltzer, an undecided GOP primary voter from Indianapolis, said Mourdock will have to work harder if he’s going to succeed.

“He needs to get better advertising out there because Lugar is too well known,” said Meltzer, 63.

Lugar has advantages that his Senate colleagues in 2010 didn’t have.

“Incumbents have a luxury of seeing what happened last time, so you won’t catch anybody off guard,” said Brian Nick, a Republican strategist and Indiana native, referring to the tea party’s primary successes in 2010. “If you’re underfunded, you sometimes benefit from the incumbent or the establishment candidate being a little lackadaisical or resting on their laurels. I don’t think that’s the case with Sen. Lugar.”

But Mourdock’s campaign said it was building up methodically to Indiana’s May 2012 primary.

“We are focused on doing what we need to do to win this race, and we are not privy to the timetable of other organizations and their decision processes,” Mourdock spokesman Chris Conner said.

Mourdock’s camp touts high-profile endorsements from Republican presidential contender Herman Cain, flat-tax proponent Steve Forbes and conservative blogger Erick Erickson. Aides say they’ve put in more time courting activists than Lugar and that will pay off in time for the state’s May 2012 primary.

The Tea Party Express, a national group, recently endorsed Mourdock shortly after a group of Indiana tea partyers officially approved his campaign. The conservative FreedomWorks is also set to endorse Mourdock on Oct. 21, said a Republican aide familiar with the group’s upcoming endorsement; that aide spoke on the condition of anonymity because the aide was not allowed to speak publicly for the group.

There are significant holdouts, though.

The Club for Growth, which earlier this summer poured thousands of dollars into ads attacking Lugar, hasn’t endorsed Mourdock. The group’s spokesman, Barney Keller, said his organization hadn’t made a decision on the race.

South Carolina Sen. Jim DeMint, a conservative kingmaker, has stayed out of the race because Lugar was DeMint’s mentor when DeMint was first elected.

Those holdouts have hurt Mourdock most in the pocketbook. Lugar practically has the state’s entire established donor base committed to him and has a huge cash advantage to show for it. Neither campaign’s report for the most recently completed fundraising quarter was available from the Federal Election Commission — campaigns must file them by Saturday — but as of July, Lugar had $3.5 million to spend compared with about $215,000 for Mourdock.

GOP operative Ryan Erwin said Mourdock will have to show he is a good candidate running a good campaign before voters unseat Lugar.

“Tea party values are always electable … but a bad candidate or a bad campaign is never going to win,” Erwin said.