House Republican leaders on Wednesday pressed ahead with their plan to hold an evening vote on their party’s budget blueprint, but the fate of the measure to unlock President Trump’s spending and tax cuts was in doubt amid a revolt among hard-line conservatives.

The resolution scaled a key hurdle Wednesday morning when the powerful House Rules Committee approved a measure that would allow it to go to the floor. G.O.P. leaders argued that time was of the essence to push it through and get started on Mr. Trump’s agenda, while Mr. Trump stepped up the pressure on Republicans to back it.

“Close your eyes and get there; it’s a phenomenal bill,” Mr. Trump told lawmakers Tuesday night at a fund-raising dinner in Washington. “Stop grandstanding.”

But a number of anti-spending House Republicans said they planned to defy the president and oppose the measure, arguing it would add too much to the nation’s debt.

“You cannot have a one-way ratchet on tax cuts and ignore the spending side of the ledger,” Representative Chip Roy of Texas said. “And my colleagues in the Senate, for sure, and some in the House on this side of the aisle, want precisely that. The Senate budget is all tax cuts and no spending cuts. Now we’re told, ‘Trust us, there’s a promise.’”

If all Democrats were to vote together, Speaker Mike Johnson could afford to lose no more than three Republicans.