Updated: 5:51 p.m. | The House is set to vote Thursday on Trade Promotion Authority, with GOP leaders employing procedural maneuvers and indirect promises to make sure the bill eventually gets signed into law.

Pro-trade lawmakers are moving ahead with a vote on TPA without Trade Adjustment Assistance, which aids U.S. workers displaced by international trade.

The success of their plan hinges on whether Democrats who voted for TPA will still support that measure without immediate certainty they’ll also get TAA, which trade opponents voted down on June 12 to derail the entire package.

Obama Won’t Sign TPA Without TAA

The Rules Committee, which voted Wednesday afternoon to set parameters for Thursday floor debate on TPA, used as a legislative vehicle a bill that originated in the House and was amended by the Senate, so it can get speedy House consideration and then, upon passage, avert a procedural speed bump in the Senate.

Democrats who voted for TPA and TAA last week looked poised to support the plan, with assurances from top GOP leaders there will be a “near-simultaneous track,” as Sen. Thomas R. Carper of Delaware put it, to pass TAA.

As plans for Thursday votes on TPA solidified, Speaker John A. Boehner and Senate Majority Leader Mitch McConnell sought to quell any outstanding anxiety.

“We are committed to ensuring both TPA and TAA get votes in the House and Senate and are sent to the President for signature,” the Republicans from Ohio and Kentucky, respectively, said in a joint statement.

Boehner was offering that commitment earlier in the week, inviting pro-trade Democrats into his office for a meeting Tuesday. According to one of the meeting’s attendees, Rep. Gerald E. Connolly of Virginia, Boehner told the group of Democrats there would be a vote on TAA.

“He didn’t specify how that would happen,” Connolly noted, but he was emphatic that Boehner said, “declaratively,” TAA will pass.

Additionally, the White House is trying to take the mystery out of the equation by saying Obama will only sign TPA if TAA is also part of the trade package.

“The only legislative strategy that the president will support is a strategy that results in both TPA and TAA coming to his desk,” White House Press Secretary Josh Earnest said Wednesday.

When Connolly was informed by CQ Roll Call that the White House had made such a commitment, he was initially taken aback. If TAA was required to be part of TPA, House Democrats opposed to a prospective trade deal with Pacific nations could continue to block TPA. But then Connolly realized the president is trying to assure Democrats that passing TPA won’t come at the expense of a TAA reauthorization.

“If trust is an issue, or people want something more ironclad by way of guarantee, I think that goes a long way toward providing it,” Connolly said.

Pro-trade Democrats held a meeting among themselves Wednesday, and later in the day traveled to the White House with Senate counterparts to meet administration officials with whom their allied in this effort.

New Democrat Coalition Chairman Ron Kind, D-Wis., who has been leading the contingent of pro-trade Democrats, said Democrats were just trying to work out the process: “And we take solace in Churchill’s admonition that he’s confident that we’ll do the right thing, but only after we exhaust all other options first.”

The 28 House Democrats who voted for TPA last week are important to making sure the do-over vote is successful in their chamber, but the key is Senate Democrats.

The TPA bill cleared the Senate 62-37, with 14 Democrats voting “yes.” That bill included TAA, which was important to Democrats, and even some Republicans such as Sen. Rob Portman of Ohio. The question for the Senate is whether the assurances that TAA will accompany TPA are direct enough, or whether they’re too direct.

TAA expires in September, and even though it’s a major risk for Democrats to continue blocking reauthorization of a program they support, doing so could still stymie the trade legislation.

Republicans are hoping the House passes TPA once again, sends it over to the Senate, and then, once the Senate proves the votes are there, the House could simply pass the TAA bill already awaiting action.

Or, the Senate could follow through on the standalone TPA bill, and lawmakers could address TAA in another separate bill. The idea is that once Democrats sense the train is leaving the station on TAA, they’ll hop aboard to reauthorize a program which they overwhelmingly favor.

It’s just a matter of how well the House and Senate can work together, and how devoted the contingent of 157 House Democrats are to stopping TPA.

Niels Lesniewski and Steven T. Dennis contributed to this report.