By David Lawder and Richard Cowan
WASHINGTON, March 6 (Reuters) - Bruised but undeterred, some of the far-right Republicans who picked a fight in Congress and lost this week over funding the U.S. domestic security agency say they're just getting started.
The views of a handful of first-term conservatives who spoke with Reuters after the Department of Homeland Security battle suggest more conflict among Republicans lies ahead.
At the core of these House of Representatives members' defiance is a conviction that their duty as lawmakers lies first with constituents and the Constitution, while House Speaker John Boehner's agenda comes further down the list.
For Boehner, who was stunningly rebuked last week by these same conservatives in a pivotal vote, unifying his party for tough fiscal challenges ahead may be more difficult than ever.
"My job's not to demand where leadership should or shouldn't be. That's not even on my radar," said Representative Jody Hice of Georgia. "My job is to represent the people in my district."
A Baptist preacher who gained fame hosting a conservative talk-radio show, Hice was one of the six freshmen among 52 Republicans who voted last week to sink Boehner's last-ditch plan for a three-week extension of Homeland Security funding.
Hice and others wanted funding for the department to be contingent on blocking Democratic President Barack Obama's recent executive orders lifting the threat of deportation against millions of undocumented immigrants.
Their demand was blocked by Senate Democrats, delaying approval of funding for the anti-terrorism agency for weeks, then ultimately dropped in legislation Boehner and Democrats pushed through to fund the department with no conditions.
Representative Barry Loudermilk, another new conservative from Georgia, said many of his constituents saw Obama's order as both a violation of Congress' powers under the Constitution and an unfair issuance of work permits to 5 million illegal immigrants who would compete with them for jobs.
"A lot of our colleagues felt this was an oath-of-office vote to uphold the Constitution," he said.
The Obama administration insists it acted legally, although a federal judge has temporarily halted implementation.
'WE OWN BOTH HOUSES'
Representative Dave Brat, a small-college economics professor from Virginia, said he, like others, supported Boehner until it became apparent the speaker would back down on the immigration demands. "I am highly skeptical that we couldn't have found a way. We own both houses - and we lost," Brat said.
Several of the freshmen are joining an aggressive new bloc of House conservatives known as the Freedom Caucus, whose founding members were among the recent Republican dissenters.
Boehner and more moderate Republicans are not taking the challenge on their right flank lightly. An outside Republican group aligned with Boehner ran internet and broadcast ads against some of the conservatives this week, saying they were putting domestic security at risk.
The American Action Network had budgeted $400,000 for the campaign, but said the ads stopped when the security agency funding was approved on Tuesday. The group said the effort is the beginning of a multi-million dollar effort to promote "center-right priorities."
These will likely include a transportation funding debate, a mid-year fight over the future of the Export-Import Bank, and a battle over raising the debt limit and approving a budget.
The campaign counters well-financed conservative groups such as Club for Growth and Heritage Action, which have often urged Republicans to vote against major spending compromises and have financed more conservative candidates to challenge incumbents.
Representative Tom Cole, an Oklahoma moderate close to Boehner, said the new conservatives should read the Constitution and realize "we don't get to make the Senate do what we want."
They "need to dial back their expectations to realistic levels. I also think leaders should maybe not satisfy every demand," Cole said. (Editing by Cynthia Osterman)