(CNN) The House of Representatives narrowly passed a budget resolution Thursday that clears the path for Congress to fast-track tax reform legislation, a major victory for President Donald Trump and congressional Republican leadership.

The vote was 216-212, with 20 Republicans joining Democrats in opposing the measure.

Republicans passed the bill despite some opposition within the party over a plan to eliminate the popular State And Local Tax deduction (SALT) in the tax reform framework.

The budget includes reconciliation rules that will allow the Senate to pass tax reform with only a simple majority rather than the usual 60 to overcome a filibuster.

The Senate has already approved the bill, and while the reconciliation rules next head to the President's desk, the President does not sign the budget resolution.

Trump tweeted after the vote , "Big news - Budget just passed!"

The current tax reform framework calls for nixing SALT deductions, a tax break used by nearly one-third of filers. Cutting the deduction would help Republicans raise more than a trillion dollars to help pay for tax cuts over 10 years, making it a huge source of revenue for their overall plan to reform the tax code.

But Republicans from states like New York, New Jersey, Illinois and California argue that their constituents rely on the deduction. While some are open to making changes to SALT -- such as capping the income level at which taxpayers could use it -- others don't favor any kind of compromise and want tax writers to leave SALT completely alone.

"My solution is to take it off the table," said Republican Rep. Leonard Lance of New Jersey.

New York Republicans are skeptical

The state and local tax deduction was one of the earliest deductions that Republicans announced would be eliminated, and the uproar was swift. The House GOP is expected to unveil text of its bill next week, and members warn that there will be a dozen more changes to the tax code that will upset members and various constituencies.

While negotiations continued over SALT in a meeting shortly after the vote, leaders and high-tax state members emerged saying no deal had been struck but talks would continue.

House Ways and Means Chairman Kevin Brady told reporters he got the message that the 20 Republicans who voted no were trying to send.

"They made it clear," Brady told reporters. "They need this problem solved before they vote yes on tax reform."

Both Brady and members from SALT states were vague on details of a potential compromise, but Republicans from New York said they're still determined to prevent a total elimination of the popular deduction in their state.

"We stood firm staying 'no' as a group today to let them know we're not kidding," said Rep. John Katko.

Katko, who represents the Syracuse area, said the meeting didn't go into specifics of a possible deal. "I think we'll be OK," he said. "The bottom line is that the ball's in their court and now they know it," he told reporters.

Rep. Peter King, who represents Long Island, said there were some Republicans who voted "yes" on the budget Thursday that might not necessarily vote "yes" on tax reform down the road.

King said he would have felt better if the budget had gone down, but he said he still felt like leadership was taking it seriously -- though he wasn't entirely confident there would be a resolution in the end.

"I'm confident they're going to come back with a proposal. I just don't know how satisfactory it would be," he said.

King said he expects more meetings will be held early next week when Congress returns.

This story has been updated and will continue to update with new developments.