Congress on Monday began an uphill push to pass a new bipartisan spending agreement into law in time to avoid a partial government shutdown next week, with Speaker Mike Johnson encountering stiff resistance from his far-right flank to the deal he struck with Democrats.

Ultraconservative House Republicans have panned the $1.66 trillion agreement Mr. Johnson made with Senator Chuck Schumer, the New York Democrat and majority leader, saying it is unacceptable.

The agreement essentially hews to the bargain that Congress passed last year to suspend the debt ceiling, which the hard right opposed at the time and had hoped to scale back. It also includes $69 billion in spending that was added as a side deal, money that conservatives sought to block altogether.

“This is a total failure,” the far-right House Freedom Caucus, a group of Republicans who have proved a thorn in the side of a series of G.O.P. speakers, wrote on social media.

“I am a NO to the Johnson Schumer budget deal,” Representative Marjorie Taylor Greene, the right-wing Republican from Georgia, wrote on social media. “This $1.6 Trillion dollar budget agreement does nothing to secure the border, stop the invasion, or stop the weaponized government targeting Biden’s political enemies and innocent Americans.”

The backlash from the extreme right underscored anew that Mr. Johnson will most likely have to rely on substantial Democratic support to pass the spending bills underlying the agreement. It also raised questions about the viability of his plan to try to attract Republican backing to spending measures by inserting conservative policy dictates aimed at restricting abortion rights and what Republicans see as “woke” administration policies.

Democrats say they will fight the addition of such policy riders. If a large bloc of Republicans opposes the spending bills, the speaker will either need to drop the policy provisions to secure Democratic backing or face a shutdown.

“Democrats will not accept any Republican poison pill policy changes,” Representative Rosa DeLauro of Connecticut, the senior Democrat on the House Appropriations Committee, declared in a statement.

The result is that Mr. Johnson finds himself in a predicament similar to the one that led to the ouster of Kevin McCarthy last fall — overseeing a minuscule majority while facing a potential government shutdown and having to cut a deal with Democrats in the Senate and the White House that is certain to draw opposition and an outcry from the far right.

The parallels were not lost on some of his colleagues.

“Are we learning that negotiating with the Democrats in the White House and Senate with a slim majority is hard and you can’t get everything you want, no matter who is in the Speaker’s office?” Representative Mike Collins, Republican of Georgia, wrote on social media.

Democrats in the House and the Senate have so far expressed support for the deal, which also has backing from many Republicans in the Senate, where both parties had pushed for even more spending.

“I’m encouraged that the speaker and Democratic leaders have identified a path toward completing” this year’s spending package, said Senator Mitch McConnell, Republican of Kentucky and the minority leader. “America faces serious national security challenges, and Congress must act quickly to deliver the full-year resources this moment requires.”

The agreement, announced on Sunday, would provide a slight increase in Pentagon spending to $886.3 billion and hold other federal spending essentially flat at $772.7 billion. After the deal was struck, the Appropriations Committees in the House and the Senate went to work crunching numbers and applying those spending levels to the 12 measures that fund the government.

Four of the bills expire on Jan. 19 and the remaining eight, including legislation funding the Pentagon, would lapse on Feb. 2. To have even a chance of hitting the first deadline, the committees will have to operate at warp speed considering that the fiscal year actually began on Oct. 1 and not a single bill has even come close to passing Congress.

“We now have a framework agreement to allow us to finally begin the hard work of negotiating — and passing — full-year spending bills,” said Senator Patty Murray, Democrat of Washington and the chairwoman of the Senate Appropriations Committee.