Thanks to strong objection from Democrats, the House of Representatives on Friday rejected a major provision of a trade authority package, which President Obama lobbied aggressively for.

In a largely symbolic maneuver, the House then narrowly voted to pass the White House-backed "fast-track" trade authority bill. The Trade Promotion Authority (TPA) bill, which would allow Congress to cast an up-or-down vote on international trade negotiations without the ability to amend the deals, passed with a close 219 to 211 vote.

However, the TPA bill can't go to the president's desk without the Trade Adjustment Assistance (TAA), which the House rejected with a vote of 126-302. TAA would give aid to workers who had lost or left their jobs due because of an international trade deal.

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Democrats rejected the TAA bill as a way to foil the entire TPA package.

Ahead of the House vote, Minority Leader Nancy Pelosi, D-California, vowed to vote against TAA, and gave a speech on the floor promising to "slow down the fast track to get a better deal for the American people."

But Republican leaders maintain that TPA will still find a way forward.

"We could do it in any number of ways," House Rules Committee chair Pete Sessions, R-Texas, told reporters after the vote. "I think the Democrats need to realize that we are going to pass TPA."

White House press secretary Josh Earnest called the House vote a "procedural snafu," adding that the Obama administration plans to "continue to make an aggressive case" for the TAA legislation.

Another vote on TAA is expected Tuesday. Should it pass that time, the entire TPA package can go to the president's desk. However, should the TAA fail again, the Senate will have to attempt to pass the TPA bill again in its new form.

CBS News Producers Alicia Amling and Walt Cronkite contributed to this report.