President Obama, Friday, May 1, 2015. (Susan Walsh/AP)

President Obama is pledging to campaign for skittish House Democrats against challenges from the left if they support his massive Pacific free-trade pact, putting his political capital on the line as the administration enters a crucial stretch to win passage.

“I’ve got your back,” Obama told two dozen lawmakers from the New Democrat Coalition at the White House late Thursday afternoon, according to Rep. Gerald E. Connolly (D-Va.), who attended and is supporting the trade initiative.

“He was emphatic,” said Connolly, who is vice chairman of the New Democrats. “He wanted to make a point. He did not want anyone to leave the room without them knowing he would personally come in and do whatever he has to do for them to be reelected.”

Obama’s forceful personal push illustrates the high stakes as he seeks to bolster support in his own party for the 12-nation ­Trans-Pacific Partnership, which he has said is one of his top legislative priorities. House Republican leaders, who support the trade initiative, have said that the president needs to secure 50 or more Democratic votes to ensure passage of “fast-track” legislation that would smooth the way for the administration to complete the deal.

But only about a dozen House Democrats have firmly voiced their support, with another dozen on the fence, according to estimates from Democrats who favor the deal.

GOP leaders are looking for potential votes within two weeks, and with the window closing, the administration has revved its lobbying into high gear. Obama highlighted the trade pact during meetings with Japanese Prime Minister Shinzo Abe last week, and Obama will travel to Portland, Ore., on Friday to tout the economic benefits during an appearance at Nike’s headquarters, the White House said.

The administration has shifted from technical explanations from cabinet officials to promises of direct political support from Obama. The attention represents a substantial personal investment by the president, whose political appearances on behalf of individual House Democrats have been almost nonexistent in the past six years, as he delegated the task to Vice President Biden.

“I think it helped everybody in the room,” Rep. Mike Quigley (D-Ill.), who attended the White House meeting and supports the trade deal, said of Obama’s pledge. “It did not just help those who are undecided, but it reinforced for those who are pluses that if you come out early [in favor] it’s okay to be a ‘yes.’ ”

Rep. Jim Himes (D-Conn.), also a vice chairman of the New Democrats, said that the meeting was reserved for about 25 lawmakers who were either a “committed yes or still on the bubble” about the fast-track vote. During a 11/2-hour meeting, the lawmakers heard from Obama, U.S. Trade Representative Michael Froman, White House political director David Simas and economic adviser Jeffrey Zients.

Obama “was willing to go deep in the weeds,” Himes said. “There’s no doubt in my mind the president and his people consider this a legacy achievement.”

That Himes finds himself on the bubble, along with other New Democrats, is a sign of how much success labor leaders have had in sowing doubts about the trade legislation.

In 2011, when Obama presented trade deals with Colombia, Panama and South Korea, Himes voted yes on all three. The Panama pact had the most Democratic votes, 66, while the Colombia deal received the fewest, 31. All three were approved by Congress.

Four years later, Democrats may be able to deliver only 25 yes votes, according to interviews with lawmakers, lobbyists and aides from both sides of the aisle. That has prompted Republican leaders to question whether the president is making any headway with his own party.

“Every Democrat leader in the House and Senate are opposed to giving the president what he is asking for,” House Speaker John A. Boehner (R-Ohio) said Thursday. Obama “needs to step up his game in terms of garnering more support,” he added.

During the White House meeting, Obama did not put a number on how many Democratic votes the administration hopes to get for the fast-track bill. But the president joked about Boehner’s difficulty securing his own GOP support in past legislative fights, according to participants in the meeting.

Himes said he would spend next week meeting with his local AFL-CIO leaders in his suburban Connecticut district. He credited opponents, including the dean of his state’s delegation, Rep. Rosa DeLauro (D-Conn.), for their determination. They began an anti-fast-track campaign with a letter signed by more than 150 Democrats in late 2013.

“I think they’ve got a little catch-up to do,” Himes said of the Obama administration. “The card game started to be played a year ago.”

Sensing the stretch run, the administration on Friday released a report from the Council of Economic Advisers touting the economic benefits of liberalizing trade. The report aimed to contest the argument from labor unions and progressives that previous trade pacts, most notably the 1993 North American Free Trade Agreement, have led to significant outsourcing for U.S. companies and job losses for American workers.

“The president has really leaned into passage of this legislation. He has directed all of us to be very active, very granular-level members of the Hill,” said Commerce Secretary Penny Pritzker, who was in Los Angeles on Friday with Japan’s Abe to talk with the U.S.-Japan Council, a business group, about the merits of trade.

Of her Japanese counterparts, she added: “I’ve heard from their team how critical it is getting the deal done. . . . But this is not just about Japan. It’s about everyone wanting to know if the administration and Congress are in lockstep in terms of the objective.”