The U.S. Capitol Building is seen in Washington, U.S., August 31, 2023. (Kevin Wurm/Reuters)

(CNN) — Congressional leaders have come to an agreement on a two-tranche short-term funding bill to keep the government funded into March, a source familiar with the matter told CNN.

The new continuing resolution will fund the government through March 1 and March 8. The agreement comes just before the first funding deadline of January 19. The second government funding deadline was February 2.

House Republicans will have a conference call Sunday night to discuss the continuing resolution, the source told CNN. And the text of the resolution is expected to be posted Sunday evening, a spokesperson for Senate Majority Leader Chuck Schumer said.

Schumer and House Speaker Mike Johnson announced last weekend that they had reached an agreement on topline spending numbers, the first step in the process to fund the federal government.

Those numbers include $1.59 trillion for fiscal year 2024, with $886 billion for defense spending and $704 billion in non-defense spending. Schumer and Johnson also agreed to a $69 billion side deal in adjustments that will go toward non-defense domestic spending.

But far-right members of the House GOP conference slammed the deal and some have pushed to include border policy changes in exchange for not shutting down the government. The blowback highlights the challenge for Johnson, who is leading an extremely narrow majority.

Johnson said Friday the deal remains in place after he appeared to be at least entertaining the idea of abandoning it in meetings with conservatives.