“I offered to have them bring up a bill later, do everything I can to give that a fair hearing because I have concerns sometimes, too,” Senator Hatch said. “But on this bill we just can’t have it on there.”

Beyond the currency issue, a provision attached to the trade promotion authority bill to block trade preferences to countries involved in human trafficking would effectively exclude Malaysia, which is on the State Department’s list of worst offenders. Another provision to crack down on child labor could stop American candy makers from importing cocoa from Africa.

While the Obama administration’s greatest concern was with the Democrats, challenges also could come from the right. Senator Rand Paul, Republican of Kentucky and a presidential candidate, said he would vote against giving Mr. Obama fast-track authority.

Democrats have united around demands that trade promotion authority — which would allow the White House to present the trade deal for a straight up-or-down vote, without amendments — be paired with a series of other measures, not only to crack down on currency manipulation, but also to assist workers displaced by globalization, tighten child labor law and fortify the government’s response to unfair trade practices. White House officials have said the Pacific trade accord cannot be completed without that authority.

After the vote, the president summoned to the White House 10 Senate Democrats whom he believes he can ultimately win over, including Senator Ron Wyden of Oregon who was a co-author of the bill he helped filibuster, and Mr. Carper, his lone Democrat supporter on Tuesday’s vote.

Republicans were equally adamant that accelerated authority not be saddled with many of those demands. “This is not a game. This is about trying to accomplish something important for the country that happens to be the president’s No. 1 domestic priority,” Senator Mitch McConnell, Republican of Kentucky and majority leader, said.

At the heart of Democrats’ demands is a measure that would force the government to respond when trading partners artificially depress the value of their currency to make their exports cheaper and United States exports more expensive.