Congress is headed for several critical votes this week on President Obama’s trade agenda.

These will be the latest twists in a ­several-month saga that has seen a majority of his own party turn against him while his long-standing adversaries have been going to extraordinary lengths to find ways to help him.

For the second time in a month, the Senate will consider Obama’s much-sought Trade Promotion Authority (TPA), legislation that would grant him “fast-track” negotiating authority to complete global trade deals with limited interference from Capitol Hill. The first vote came late on the Friday of Memorial Day weekend, when 62 senators — 48 Republicans and 14 Democrats — backed Obama and thought they were done with the issue.

But then came a Democratic rebellion in the House, where Minority Leader Nancy Pelosi ­(D-Calif.) joined with the rank-and-file Democrats to block one portion of the legislative package and upend months of carefully negotiated planning.

On Tuesday, the Senate will hold a vote on the first piece of the reassembled legislative package in a move plotted by Senate Majority Leader Mitch McConnell (Ky.), House Speaker John A. Boehner (Ohio) and Obama, designed to force liberal Democrats into a box from which they will have no good option.

“And so, assuming everyone has a little faith and votes the same way they just did a few weeks ago, we’ll be able to get all of these bills to the president soon,” McConnell said Thursday evening, unveiling the plan.

Tuesday’s vote, if the same 62 senators hold together, will end any chances of a filibuster on TPA, setting up a final vote on the trade-promotion-only plan Wednesday. Immediately after that is approved, the Senate would take up legislation that is designed to increase trade with sub-Saharan nations, the African Growth and Opportunity Act, or AGOA.

That’s the very popular bill that has come to the rescue for Obama and his unusual alliance with McConnell and Boehner. It passed the Senate with 97 votes and the House with almost 400 votes, but it was slightly modified after liberal opposition in the House, so the Senate needed to reconsider the legislation.

By forcing that reconsideration of AGOA, those liberal opponents gave Obama’s trade agenda a second chance. In the House, Democrats also rebelled against new funding for a worker-retraining program, which was originally expected to win approval largely on the back of Democratic votes. Once they abandoned that bill, the entire trade measure stalled because of the way Boehner had structured the trade debate.

With Obama’s blessing, Boehner passed a TPA-only bill and sent it to the Senate for its do-over consideration this week, and McConnell took the African trade bill and set it up to be amended and include the worker-training funds.

Working closely with Sen. Patty Murray (D-Wash.), one of the 14 pro-trade-agenda Democrats and a trusted negotiator, McConnell also plans to add a provision that would help the steel industry be more competitive against global competition. That will help mollify some of the concerns from Sen. Sherrod Brown (D-Ohio), the leader of Senate opponents to Obama’s trade initiatives. But McConnell is also keenly aware of the politics in his own caucus — Sen. Rob Portman (R-Ohio), who is facing a very difficult reelection campaign in 2016, also supports Brown’s bid to help the steel industry.

McConnell and Murray bet that, after TPA passes Wednesday, they will then win on a big vote for the new bills cobbled together because they are each big for Democratic constituencies and will bring back the rebellious Democrats.

According to administration officials and senior aides in both parties, the Senate is likely to pass the AGOA bill and its accompanying parts by Thursday, sending it to the House for its final consideration.

There, supporters of Obama’s trade agenda believe that liberals will be finally boxed in: The fast-track bill they actually oppose will be on the president’s desk awaiting his signature. Their initial hostage — the worker-training program — is an initiative the liberals actually support, and it would now be tied to two other programs they back: AGOA and the steel industry competitive issue.

“We cannot allow AGOA to expire, so if there’s something that is attached to AGOA, it has to be something that we know will get through both houses. We’re in conversations,” said Rep. Gregory W. Meeks (D-N.Y.), one of 28 House Democrats to vote for TPA.

Pelosi has largely deflected questions about how she would guide her caucus if late this week they were faced with a take-it-or-leave-it vote on that legislation. Also quiet on the issue has been Rep. Rosa L. DeLauro (D-Conn.), who has led the liberal rebellion against Obama in the House.

“As it stands today, a path forward for this legislation is unclear,” DeLauro said, expressing hope that some Senate Democrats would hold out their support in exchange for a guarantee that the controversial Export-Import Bank would be reauthorized.

McConnell remained optimistic that every piece of the trade agenda could be sent to the president before Congress goes on a 10-day break over the July 4 holiday, slated to begin Friday.

“That would be quite an achievement,” he said. “All it’s going to take is some hard work and some faith in one another.”