A REPUBLICAN PRESIDENT'S REPUBLICAN LEGACY:

The administration's most significant policy goal right now is to secure the Trans-Pacific Partnership, which would be the largest trade deal since the 1994 North American Free Trade Agreement.

The accord would pull in a dozen nations from Peru to Vietnam, lowering tariffs and imposing new regulations on labor and environmental standards along the Pacific Rim. Officials have lobbied members of Congress for months to get it done. But many Democrats oppose the deal, believing that Nafta cost thousands of American jobs and continues to depress wages.

"We have been told for years that these things will benefit the economy, and I am not sure it is true," said Senator Bob Casey of Pennsylvania, who is among at least a half-dozen Senate Democrats who have denounced the proposed agreement. "I think the administration knows where people like me are."

In the House, large numbers of Democrats have joined Republicans to oppose separate legislation that would give the president "fast-track" authority to negotiate trade treaties that Congress could approve or reject but not amend.

"There is no earthly reason to take congressional authority out of trade bills," said Representative Louise M. Slaughter, Democrat of New York, who opposes the trade proposal. Acknowledging that she was siding against Mr. Obama, she added: "I represent the people of the 25th District of New York. I like having a Democratic president, but I don't agree with him on this."

While Representative Nancy Pelosi of California, the House minority leader, has said she "wants to get to yes" for Mr. Obama on trade, many of her members expect her to stick with them in the end. Ms. Pelosi "has been a leader on this," said Representative Rosa DeLauro, Democrat of Connecticut. "She has always been a supporter of congressional authority."

Last week, the administration's formal request for authorization of military action against the Islamic State appeared headed for collapse, in many respects because Democrats found the language of the agreement too open-ended.

"What I think Democrats are not willing to do," said Senator Robert Menendez, Democrat of New Jersey, "is to give this or any other president an open-ended authorization for war." To be sure, plenty of Republicans have criticized the administration's proposal as well, saying it is actually too constrained.

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