Sens. Al Franken (D-Minn.), left, and Bernie Sanders (I-Vt.) arrive in the underground subway system for a vote at the Capitol on Thursday. (Jonathan Ernst/Reuters)

President Obama reversed an embarrassing political defeat on Thursday when the Senate voted to advance his controversial trade agenda, which remains contentious among the president’s traditional supporters.

Obama cleared a key hurdle as senators voted to open debate on “fast track” legislation that would give him greater negotiating authority and could pave the way for approval of the wide-ranging ­Trans-Pacific Partnership trade accord.

Earlier in the week, Senate Democrats had balked at moving forward with the fast-track legislation, demanding guarantees that it provide strong enforcement provisions, including measures aimed at curbing currency ma­nipu­la­tion.

Republican leaders agreed to vote on a separate enforcement bill, and 13 Democrats joined 52 Republicans in a procedural vote to move forward with fast-track legislation, providing the 60 votes necessary to break what had been a united Democratic filibuster.

The vote was a boost for Obama, who summoned 10 pro-trade Senate Democrats to the White House on Tuesday after an initial test vote failed, hastening the compromise that lends new momentum to his high-stakes trade campaign. At a Camp David news conference Thursday, he thanked senators for moving forward with what he called a “smart, progressive, growth-promoting trade deal” and lauded most of the enforcement provisions.

Democratic infighting over an Asia-Pacific trade deal is exposing both personal and policy issues between Sen. Elizabeth Warren (D-Mass.) and President Obama. The Post's Chris Cillizza explains the feud. (Tom LeGro/The Washington Post)

“Despite the fact that there have been very genuine problems with some trade deals in the past, the approach we are taking here, I think, is the right one,” he said.

Earlier on the Senate floor, Sen. Ron Wyden (D-Ore.), who negotiated the fast-track bill with congressional Republican leaders but then stalled it this week over the enforcement concerns, declared “a new day for trade policy.”

“You can pack trade agreements full of lofty goals and principles. You can amass all of the enforcement ideas you might want. But it doesn’t do any good,” Wyden said, “if you don’t have real enforcement tools.”

The enforcement bill passed Thursday 78 to 20, and a second piece of the trade package, extending aid programs for developing countries, passed 97 to 1. But the bulk of the Senate debate is expected next week, following the afternoon procedural vote on proceeding with the fast-track bill, also known as “Trade Promotion Authority,” or TPA.

By passing the bill, Congress would relinquish its ability to amend trade deals negotiated by the executive branch, leaving them subject to a simple up-or-down vote. The 12-nation ­Trans-Pacific Partnership, or TPP, is the most ambitious deal likely to come up for consideration.

Ratifying the TPP, which enjoys broad support from Republicans, is a cornerstone of Obama’s second-term agenda, with a GOP-controlled Congress unlikely to move forward on other key priorities. But the trade legislation faces fierce opposition from most congressional Democrats, who have been rallied by the most loyal constituent of the party’s political base: labor unions.

“This will be a very, very major vote on the scorecard,” AFL-CIO President Rich Trumka said Thursday in a discussion with Washington Post reporters and editors. “It means so much to working people that, on this one, if you are against us, you are against us.”

Democratic fast-track skeptics pledged Thursday to offer amendments — including enforcement and currency ma­nipu­la­tion provisions — to that bill amid warnings from Republicans and the Obama administration that they could constitute “poison pills” tanking overall support.

The White House said in a statement that the currency ma­nipu­la­tion language passed in the separate bill “would undermine our international efforts to address this issue, raise highly problematic questions about consistency with our international obligations, lead to other countries pursuing retaliatory measures that could hurt our exporters, and be difficult to administer.” Obama said Thursday that the provision could have a “blowback effect on our ability to have our own monetary policy.”

Republican leaders said Thursday they hope to finish consideration of the trade legislation by the end of next week, before a week-long Memorial Day recess. Then the debate would move into the House, where Democratic opposition is more robust and a significant bloc of Republicans also opposes granting fast-track authority.

Trumka decried the move to separate the currency provisions from the fast-track deal. Those provisions could lead to the imposition of punitive duties on goods imported from countries found to be depressing the value of their currencies,

“What do you think happens to it when it gets to the House? It’s DOA,” he said. “Unless it all goes together, it’s not going to work and we’re not going to be for it, and we’re going to be hard-edged about it.”

House Speaker John A. Boehner (R-Ohio) offered support for that view Thursday. “To think that Congress can legislate what currency valuations are between countries is almost laughable,” he said at a news briefing.

Sen. Richard J. Durbin (D-Ill.), the minority whip and a free-trade skeptic, dismissed suggestions that Democratic leaders had undermined the opposition to fast track by agreeing to a separate enforcement bill, which could die in the House or be vetoed by Obama.

“We’re going to come back to it next week” as an amendment on the fast-track bill, he said. But he also acknowledged that Senate Majority Leader Mitch McConnell (R-Ky.) may take steps to limit amendments in order to complete Senate consideration of the trade bills before Memorial Day.

Anti-fast-track Democrats said they will continue to look for opportunities to toughen the bill. “I think we still have opportunities for debate, and we’ll be doing that next week,” said Sen. Gary Peters (D-Mich.). “Currency is a significant issue for the auto industry that has to be addressed, so that is my focus.”

Senate Republicans set up Monday votes on two amendments — one Republican, one Democratic — before finishing their week’s work Thursday evening.

“What I don’t want to happen is that we get crammed up and then people feel like they’ve been shut out of the process and get bent out of shape,” said Sen. John Cornyn (R-Tex.), McConnell’s top leadership deputy. “There are actually some people who don’t want to pass a bill, and they’re happy to cause as many impediments and obstructions as they can.”

Sen. Charles E. Schumer (D-N.Y.), an outspoken proponent of the currency ma­nipu­la­tion measure, said he was not dead-set on attaching it to the fast-track bill. But he said the enforcement bill, which includes currency language, may need to move in concert with fast track.

“I don’t think there are enough votes in the House to pass [fast track],” Schumer told reporters Thursday. “It may be that some of them will say, ‘Maybe I’ll go with it if currency becomes law.’ . . . It may well be that currency is needed to get the TPA bill through, given the reluctance of Democrats.”

Among the factors driving that reluctance is labor’s suggestion that it will abandon campaign support for fast-track supporters in Congress. While union endorsement decisions are made on the state or local level, Trumka said he expects the issue to trump most other considerations.

“If I were predicting, I would say some people would probably have primary opponents because of this vote,” Trumka said. “I’m not threatening that — I’m just saying that is something that will happen. . . . We’re talking about this being an issue that we believe will be detrimental to working people for an indefinite future. It will suppress our wages indefinitely. And we’re going to fight.”

Trumka said Democrats who vote for fast track cannot count on the inclusion of worker assistance or their other pro-labor votes to retain their labor support.

“We’re not going to overlook it,” he said. “We’re not going to walk away and say, ‘Oh well.’ . . . We’re going to use every arrow in our quiver.”

Paul Kane and Kelsey Snell contributed to this report.