The scramble to avoid another government shutdown has stalled out as an end of Friday deadline looms for Congress to strike an agreement on border security.

Efforts to prevent the second partial funding lapse of the year have hit a roadblock, a Democratic aide told CNBC on Sunday. The Republican side also showed concerns. "The talks are stalled right now," Sen. Richard Shelby, R-Ala., the top GOP negotiator on a conference committee trying to hash out an immigration spending deal, told "Fox News Sunday."

An argument over how best to allocate border security money now threatens to reopen fresh wounds for the 800,000 federal workers who missed two paychecks during a record 35-day shutdown in December and January. Even as both major parties show no appetite for another closure, the ongoing dispute over immigration policy could stifle efforts to keep the government running.

Top appropriators plan to meet Monday afternoon as they try to salvage a last-minute deal, three sources told CNBC. Shelby, chairman of the Senate Appropriations Committee, House Appropriations Committee Chairman Nita Lowey, D-N.Y., Sen. Patrick Leahy, D-Vt., and Rep. Kay Granger, R-Texas, will meet.

The meeting is intended to be private, and the lawmakers are not expected to discuss details such as dollar amounts or the number of detention beds — the latest sticking point in talks. They see it as an opportunity to agree to move ahead with talks. The appropriators are already behind their desired timeline: one source said they originally hoped to release an agreement by noon Monday.

Ahead of the meeting, a House Democratic aide said some Republicans have floated the possibility of a continuing resolution to fund the Department of Homeland Security through the end of the fiscal year on Sept. 30. Democrats will not back such a spending plan, as they argue it would allow the Trump administration to put more money toward physical barriers and detention beds, the aide said.

President Donald Trump has appeared to back off his demand for a full $5.7 billion to construct his proposed border wall — which led to the previous funding lapse. However, he has still made the case for physical barriers on the U.S.-Mexico border, and will do so again during a rally Monday in El Paso, on Texas' western edge.