The goal is to block the omnibus proposal in both chambers by Friday, a move that would leave Congress little time to consider its content.
Some sticking points in the omnibus negotiations included disagreements over immigration provisions, abortion language and veterans issues, as well as other points.
It remains possible that Congress will need to adopt another short-term stopgap to keep agencies afloat in order to give more time to the Covid relief talks.
It comes after the House and Senate passed a week-long rolling resolution that would fund the government until December 18, which would buy time for these negotiations to continue.
When it comes to relief from Covid-19, there are still many disagreements between the two parties over what the language should include. Democrats wonder whether to abandon aid to states and cities to get a lightened Covid-19 relief deal or whether to make a last ditch attempt at a bigger plan even if it risks a deal in the closing days of the 116th Congress.
This story was updated with additional developments on Monday.