He was one of four Republicans stripped of their committee assignments last year, and one of a dozen Republicans who did not vote to re-elect Representative John A. Boehner, Republican of Ohio, as the House speaker.

“They never ever vote yes,” a Republican familiar with the dynamics of the House said on the condition of anonymity for fear of offending a fellow Republican. “There’s always some more perfect thing that’s completely impractical that they insist upon. They wind up pulling policy in the opposite direction from their stated goal, because if you are trying to pass something and you know they’re going to vote no, you have to go to the left to pick up votes.”

Mr. Amash says that he is simply representing his constituents, and that he frequently votes with his party. Mr. Amash has broken with a majority of his Republican colleagues 27.5 percent of the time, the most of any House Republican.

“We’re filling a gap in leadership,” Mr. Amash said. “There have been a number of important issues that have come up where our constituents are asking us to take a position to present their perspective.”

Only midway through his second term in Congress, Mr. Amash is already considering a bid for Michigan’s open Senate seat in 2014, though he is not expected to announce his decision until the fall. Liberty For All, a political action committee that supports candidates with libertarian principles, has already pledged “six figures” to support a Senate bid by Mr. Amash.

“Democrats are mad at Obama, Nancy Pelosi and Harry Reid, and Republicans are mad at the Republican leadership,” said John Ramsey, a co-founder of the PAC. “So it’s a powder keg for libertarianism.”

That libertarian streak surfaced quickly in July after revelations of sweeping surveillance by the National Security Agency.