Obama’s trade agenda collapsed in the chamber Friday when House Democrats killed an extension of a program that aids workers displaced by imports — a Democratic priority since the Kennedy administration. The maneuver effectively froze progress on an attached measure that would have given the administration the fast-track power to wrap work on the trade mega-deal linking economies from Japan to Peru, officially the Trans Pacific Partnership.

House GOP leaders used a procedural move Friday to buy a second chance at the package, which came due today. But the White House wasn’t able to make a dent in the opposition over the weekend, so rather than force another doomed vote, Republicans decided to buy some extra time. Speaker John Boehner (R-Ohio) told reporters Tuesday the decision came after several conversations with Obama about the way forward.

By all accounts, the pro-trade forces have yet to strike on a winning strategy for reviving the effort. They do have options. House Minority Leader Nancy Pelosi (D-Calif.) hinted at one on Friday, just hours after her last-minute defection helped seal the package’s fate. In a letter to colleagues, she suggested that new infrastructure spending would help loosen Democratic screws on the trade measure. Her lieutenant, House Minority Whip Steny Hoyer (D-Md.), endorsed the possibility Tuesday morning, telling reporters that linking the package to highway funding that likewise expires in six weeks could convert “a number” of Democratic votes.

Other Democrats on either side of the widening intra-party rift are less sanguine that adding sweeteners can salvage the measure. “This is not the era of horse-trading,” said Rep. Gerry Connolly (D-Va.), one of only 28 Democrats who backed granting Obama fast-track authority. And Jan Schakowsky (D-Ill.), a stout free-trade skeptic, said the administration would find a “solid majority is not going to be susceptible to some sort of a buy-off.”

Instead, Schakowsky said, the White House should view its stumble as an opportunity to invite Democratic critics back into the fold and work on addressing their substantive problems with the pending trade deal itself. Specifically, she said the administration should scrap a corporate dispute-resolution process that Sen. Elizabeth Warren (D-Mass.) has helped elevate to liberal flashpoint, as well as protections for big pharmaceutical companies.

An Obama booster since before he won his U.S. Senate seat, Schakowsky said she’s not heard from him since the trade fight started but would be reaching out now. “It’s really painful for me as a long time friend of the president’s and a long time supporter of the president to be on the other side, but essentially everybody who got him elected, the main players, are on the other side,” she told Fortune in an interview. “And this notion that I think the administration has that no matter what they do, we’re going to be against a trade agreement, that’s just not the case.”

But the White House is likely to want to exhaust its alternatives before granting concessions on the meat of the deal. Administration aides huddled Tuesday morning with two dozen pro-trade House Democrats to discuss the path forward. Connolly, who attended, said it didn’t yield any breakthroughs. “This is a work in progress, so we’ll know more soon,” he said.

One possibility involves separating the fast-track authority from the worker assistance provision that House Democrats used to sink it. That would require trade supporters to hold together a fragile majority that approved fast-track on Friday — by a 219-211 margin — and send it back to the Senate, since the upper chamber voted on a single package that combined the two. Then, pro-trade forces would need to stem Senate Democratic defections on a package stripped of the worker help, while enduring slings from a reenergized labor movement riding high on its success freezing Obama’s trade agenda in its tracks.

The din that the AFL-CIO and its allies have sustained against the trade pact likely means that a drawn-out process doesn’t favor the White House. But in the short term, at least, they can at least expect some grace from their foreign counterparts in the Pacific Rim deal negotiations. “As perplexed as we all are about what happens here, imagine what it looks like overseas,” said Rep. Tom Cole (R-Okla.), a member of the House Republican whip team. “It’s like American football: Nobody really understands the rules who didn’t grow up here. Most of the foreign countries just chalk it up to, ‘Well the Americans are working it, let’s just see what happens.’”