WASHINGTON — An odd marriage of convenience between liberal Democrats and Tea Party Republicans is squeezing President Obama on his ambitious trade agenda, forcing the White House and top Republicans to fight a two-front war on an international economic effort the president hopes to secure before he leaves office.

An alliance between the likes of Representatives Louie Gohmert and Dana Rohrabacher — two of the House’s most conservative members — and Rosa DeLauro and Louise Slaughter — ardent liberals — is unlikely enough. But as the political fringes expand on each end, they are challenging another strange-bedfellows alliance between Mr. Obama and Republicans like Representative Paul D. Ryan and Senator Orrin G. Hatch, who have joined together in a push to secure “fast-track” trade promotion authority before the administration completes a major trade agreement with 12 partners along the Pacific Rim.

“This president has tried to rule by dictate in a number of arenas,” said Mr. Rohrabacher, explaining the right’s reluctance to now give Mr. Obama the authority to complete a trade deal under the traditional rules that offer Congress only an up-or-down vote, with no power to amend it. “He’s issued executive orders in a way that is totally out of sync with what executive orders are supposed to be about. A lot of people think this president has been much more aggressive in centralizing power.”

Ms. DeLauro, not usually an ally of Mr. Rohrabacher’s, struck a similar theme.

“We have trusted and trusted for years and years, and it’s only been to the detriment of American workers,” she said. “Members of Congress are fed up with this. The trust factor, whether it’s Barack Obama or anyone else, is not there any longer.”