ATLANTA — President Obama hailed the historic 12-nation Pacific Rim trade deal completed here Monday as an accord that "reflects America's values," but within hours the administration had turned from the negotiating table to selling the agreement on Capitol Hill, a reflection of the harsh political climate the controversial pact is expected to face in Congress.

Obama pledged that the ­Trans-Pacific Partnership (TPP), the largest free-trade agreement in a generation, would open new markets for U.S. goods and services and establish rules of international commerce that give "our workers the fair shot at success they deserve."

But almost immediately there were signs of the tough fight ahead to win final ratification from Congress next year. Lawmakers from both parties criticized the pact as falling short in crucial areas, raising the prospect that the White House could lose the support of allies who had backed the president's trade push earlier this year.

"Closing a deal is an achievement for our nation only if it works for the American people and can pass Congress by meeting the high-standard objectives laid out" by lawmakers in the spring, said Sen. Orrin G. Hatch (R-Utah), chairman of the Senate Finance Committee. "While the details are still emerging, unfortunately I am afraid this deal appears to fall woefully short."

Monday's announcement that trade ministers had reached consensus on the deal, after five days of negotiations, started the clock on the final stages of winning approval from national legislatures. The United States, where the 2016 presidential campaign is underway, is not the only nation where political turbulence could affect completion of the deal.