WASHINGTON – Self-proclaimed tea party leader Michele Bachmann’s bid for a top Republican post in the House received a cool reaction Thursday from Speaker-to-be John Boehner, an early test of how GOP leaders will treat the anti-establishment movement’s winners in Tuesday’s elections.

“Constitutional conservatives deserve a loud and clear voice in leadership!” Bachmann, R-Minn., who founded the Tea Party Caucus, said in a one-paragraph Facebook announcement that she is running for GOP conference chairman.

House Republican leaders don’t disagree. But that doesn’t mean they want the hyperbolic Bachmann being a spokeswoman for the new majority during the 2012 election cycle.

Boehner, aware of the role tea partiers played in making him the next House speaker, is endorsing no one. His lieutenants are lining up behind Rep. Jeb Hensarling of Texas, leaving no doubt that Hensarling — and not Bachmann — is the leadership favorite to chair the GOP conference.

“There are few who have done as much for the Republican team as Jeb,” the expected House majority leader, Eric Cantor of Virginia, said.

Departing conference chairman Mike Pence of Indiana also endorsed Hensarling, calling him “one of the most principled conservatives in Congress.” Pence is stepping down to pursue a possible gubernatorial or presidential bid in 2012.

Rep. Steve King, R-Iowa, said Bachmann is a talented communicator who would represent the views of the more than 30 newly elected tea partiers who helped return the House majority to Republicans.

“The new majority-makers need to have a voice inside the leadership team,” King said. Hensarling is said to have lined up dozens of endorsements for the leadership elections, set to take place after Congress returns Nov. 15.

Boehner has been careful to avoid alienating either one.

Ohio Republican “considers Reps. Hensarling and Bachmann both good friends and he knows they will make big contributions to the success of our team in the 112th Congress.” said Boehner spokesman Kevin Smith..

Hensarling is said to have lined up dozens of endorsements for the leadership elections scheduled to take place after Congress returns Nov. 15.

The tea-leaf reading of the tea party’s role in the next Congress illustrates the delicate choice facing the incoming GOP House leaders: How, if at all, to acknowledge and reward the freshman lawmakers who call themselves tea partiers and were instrumental in returning the House majority to Republicans.

The relationship, by definition, is awkward. Many of the tea partiers won their seats by campaigning against entrenched Washington power brokers, like Boehner, Cantor, Pence and other senior Republicans. Some want to keep the channels open to what’s expected to be a distinctly uncompromising freshman class.

House GOP leaders have varying views of whether any overture, symbolic or otherwise, is warranted. Still in the discussion stages is a proposal to establish a sort of at-large leadership post for a representative of the freshman class, but no decision has been made, according to GOP officials who spoke on condition of anonymity.

Bachmann’s contribution to the GOP’s election gains is undisputed and GOP leaders widely praise her fundraising prowess. The Minnesota Republican is the House’s top earner, bringing in $11 million in the two-year election cycle for her own campaign.

But she’s also made GOP leaders cringe multiple times in the last two years with over-the-top and uninformed statements.