WASHINGTON — His successor, whether Democrat or Republican, opposes it, as does most of his party. Delegates at the Democratic National Convention waved signs saying “T.P.P.” slashed by a bold line, while the Republican Party platform opposed any vote on it in Congress this year.

Yet President Obama is readying one final push for approval of the Trans-Pacific Partnership, the largest regional trade agreement ever, between the United States and 11 other Pacific Rim nations. And though the odds may be long, a presidency defined by partisan stalemate may yet secure one last legacy — only because of Mr. Obama’s delicate alliance with the Republicans who control Congress.

“Both parties have candidates who have very strong rhetoric against trade,” said Representative Kevin Brady, Republican of Texas and chairman of the House Ways and Means Committee, which is responsible for trade. “Nonetheless, we can’t grow America’s economy unless we’re not merely buying American but selling American all throughout the globe.”

Still, he added, timing a vote “is absolutely dependent on support for the agreement.”

Although the administration’s push will begin in September, no vote on the accord will occur before the election. Just as the White House and congressional Republican leaders mostly agree on the economic benefits of trade, they have parallel political interests in delaying debate.