A second senior member of U.S. President Barack Obama's party spoke out on Wednesday against a proposal to give the White House power to fast-track trade deals, delivering another blow to the chances of getting the bill through Congress quickly.

House Democratic leader Nancy Pelosi told a union rally she opposed legislation currently before Congress to grant the U.S. administration so-called Trade Promotion Authority (TPA) to seal trade deals.

"No on Fast Track ... out of the question," she told the United Steelworkers and the BlueGreen Alliance, according to a transcript of remarks provided by her office.

Pelosi, who voted against the last fast-track bill before the House but has supported some free trade deals, told reporters later that her comment was not "a rejection of the president's trade agenda. It is a rejection of the current form of (the bill)."

"I have worked with many of our colleagues to try to find some common ground, but in its present form, it is unacceptable," she said at the start of a retreat in Cambridge, Maryland, for House Democrats.

Her opposition follows a warning by the top Democrat in the Senate, Harry Reid, not to push the TPA bill, which some Democrats fear could lead to trade deals that hurt local jobs and industry and could cost them support in November elections.

Republicans, who are generally more favorably inclined toward free trade and its benefits for business, have seized on the issue to call on Obama to do more to drum up support for the bill and highlight the differences among Democrats.

Supporters of fast-track power say trading partners involved in negotiating two massive trade deals with the United States will not put their best offers on the table unless they know the final agreement can be submitted to Congress for an up-or-down vote, without amendments.

A drawn-out passage through Congress might put back the timetable for finalizing the Trans-Pacific Partnership with 11 other Pacific Rim nations, which U.S. negotiators had hoped to wrap up by April.

But others note negotiations started on both the TPP and the Transatlantic Trade and Investment Partnership with the European Union after the last fast-track power expired in 2007 and say the lack of a deal has not been a noticeable hurdle to progress.

The expiry of TPA left in limbo free trade pacts that were agreed with South Korea, Panama and Colombia. But all three eventually passed Congress in 2011, though the agreement with South Korea was partly amended.

Pelosi's opposition will make it difficult to push ahead with the current bill in the House, where the legislation lacks a Democratic co-sponsor, and its future in the Senate is also uncertain.

Representative Sander Levin, the top Democrat on the House Ways and Means Committee, has said the bill does not go far enough to involve lawmakers in trade talks or to prevent currency manipulation by trading partners. He is working on an alternative version.

Pelosi said currency manipulation was "a smack in the face of American workers," leaving open the option she might support a version of the bill with tougher currency provisions.

In the Senate, Democratic sponsor Max Baucus is leaving to become the next U.S. ambassador to China, and the expected next head of the Senate Finance Committee, Ron Wyden, has expressed reservations about the legislation as drafted.