The Senate’s top Republican said Thursday that the sweeping 12-nation Pacific Rim trade deal championed by President Obama will remain on ice until another president revives it.

And with both current presidential nominees opposed to the deal’s ratification, that could be the death knell for the Trans-Pacific Partnership, barring a major shift from Democrat Hillary Clinton or Republican Donald Trump.

“Since they negotiate the deals and they send them up, the president is a big, big player in trade,” Senate Majority Leader Mitch McConnell (R-Ky.) said at a news conference Thursday. “If we were going to have another discussion about trade, it would have to be led by whoever the next president is.”

Obama has made a renewed push in recent months for congressional ratification of the trade agreement, known as the TPP, with an eye toward persuading Congress to hold a vote on the deal in the post-election lame-duck session. The president has called the largest regional trade and regulatory deal in history one of his top economic priorities and a crucial strategic initiative in the fast-growing Asia Pacific, where the administration has sought to hedge against China’s growing influence.

McConnell, who had previously ruled out a lame-duck trade vote, reiterated that position Thursday.

“Let’s just be honest about the political environment,” he said. “I believe if it were brought up this year it would be defeated anyway — leading you to raise the obvious question: If you’re interested in America still being in the trading business in the future, in what way is it advantageous to have a trade agreement go down?”

Obama aides have suggested that McConnell is reluctant to move forward on trade ahead of the elections to protect vulnerable Republican incumbents and GOP candidates from having to weigh in on the pact in manufacturing-heavy swing states, such as Ohio and Pennsylvania. But the administration officials have privately expressed hope that McConnell will change his mind after the election.

“The choice facing members of Congress is clear: either we can set the rules of the road for global trade in the Asia-Pacific region or we can cede that responsibility to China,” White House spokeswoman Brandi Hoffine said. “The president believes that America should set those rules.”

The TPP covers nations that represent 36 percent of global gross domestic product, including Japan, Mexico, Canada, Singapore, Malaysia and Vietnam. The accord has drawn broad endorsements from influential business groups, such as the U.S. Chamber of Commerce and the National Association of Manufacturers. Obama met in the Oval Office two weeks ago to discuss its merits with bipartisan political and business leaders, including former New York City Mayor Michael Bloomberg (I) and Ohio Gov. John Kasich (R), both of whom support the pact.

In the administration’s most recent public push, Secretary of State John Kerry said in a speech Wednesday that a failure to ratify the agreement would carry “serious consequences” for American foreign policy.

“We can’t withdraw from the TPP and still be viewed as a central player in the Pacific Rim and an undisputed force for peace and prosperity across the globe,” he said. “Our partners worldwide need to know they can always look to us for principled leadership, with no uncertainty and no doubt.”

There is little stomach among congressional Democrats to push through the TPP anytime soon. One of the TPP’s leading Democratic supporters, Sen. Ron Wyden (D-Ore.), said ratification “is really going to come down to only one question: Does Mitch McConnell put this in play?”

Both McConnell and House Speaker Paul D. Ryan (R-Wis.) generally favor free trade, and both supported a bill that passed last year granting Obama and his successor special “fast track” authority to negotiate trade agreements such as the TPP.

But that was before trade became a major issue in the presidential race, pushed front and center by candidates such as Trump and Sen. Bernie Sanders of Vermont, who ran unsuccessfully for the Democratic nomination. Both of them blame free-trade agreements for the loss of working-class American jobs.

Clinton had been a forceful advocate for the TPP while serving as secretary of state during Obama’s first term, calling it crucial to the administration’s strategy to “rebalance” American foreign policy attention and resources towards Asia. But Clinton announced her opposition after the deal was finalized last fall during her closer-than-expected primary fight against Sanders.

Ryan has also voiced skepticism on the TPP’s prospects, despite his personal support for trade. Some Republican lawmakers typically inclined to support trade deals have objected to some provisions in the TPP that could hurt tobacco and pharmaceutical companies.

“The Obama administration negotiated a deal that cost them dozens of votes in Congress,” Ryan said in a Wisconsin Public Radio interview in August. “The votes are not there, they have to fix this agreement and renegotiate some pieces of it if they have any hope or chance of passing it, and I think that the sand is running through the hourglass pretty fast.”

Wyden said he was skeptical that the deal could be reopened to address those concerns, and warned that any attempt to appease Republicans would generate Democratic opposition. “I am going to be fighting that every step of the way,” he said.

McConnell said Thursday that the United States needs to “work our way back into the trade business,” but he acknowledged “that’s become a very, very difficult thing politically. That will require presidential leadership from the next president.”

He noted that “fast track” authority will continue throughout the next president’s term and that there is no set timeline for the TPP’s ratification. “America has been a great trading country going back to the founding of the country,” he said. “But right now, it is politically toxic, and I don’t think the Congress is ready to tackle it in any positive way.”