But the budget bill the Senate passes will likely be very different from the one the House approved last week and that means lawmakers will have only days to work out a compromise acceptable to both chambers of Congress and the White House before the fiscal year ends.
The House bill funds the government but strips funding for Obamacare, a proposal the Democratic Senate and White House reject. The Senate is expected to strip the Obamacare provision from the House bill, which could effectively stalemate negotiations over the budget as the deadline nears.
Republicans believe this is their final opportunity to block the new health care law, which polls show remains unpopular with the public even though it's expected to be fully implemented by January.
More than a dozen Senate Republicans have pledged to reject any budget bill that includes money for Obamacare. But 41 Republican votes would be needed to block such a bill, making it unlikely that the faction will prevail.
Republican senators -- including John McCain, of Arizona, Lindsey Graham, of South Carolina, and Lamar Alexander, of Tennessee -- have said they will not allow the government to shut down because of the Obamacare funding.
Sen. Ted Cruz, R-Texas, one of the leaders of the defunding movement, on Sunday called on his GOP colleagues to "stand side-by-side" with House Republicans, who voted to strip the health care funding.
Cruz said on "Fox News Sunday" that any vote to take up the Senate measure, which will eventually be stripped of the defunding language, "is a vote for Obamacare."
The Senate will hold several key votes on the funding bill, with the first vote among the most important because it will determine whether leaders have the 60 votes they'll need to begin debate on the measure. Another 60 votes will be needed to cut off debate, when Senate Majority Leader Harry Reid, D-Nev., will likely introduce the amendment that strips the Obamacare provision with a simple majority vote, a move that allows Democrats to strip the provision without Republican support.
House Republican leaders will be working behind the scenes to devise any amendments necessary to counter whatever the Senate passes.
Among the ideas under consideration is an amendment that would subject congressional staff to the same terms of the health care law as the rest of the public, which would force them to pay much more for their coverage.
Cruz wants House Republicans to scrap the Reid budget bill and send to the Senate a series of appropriations bills that fund individual government agencies but excludes the branch that funds the health care law.
House Republicans have kept their strategy under wraps for now, saying they want to see what the Senate does.
The House will spend most of its time this week on less urgent legislation, including a land exchange bill that would open up hundreds of acres in Arizona for copper mining.
That bill, the Southeast Arizona Land Exchange Conservation Act of 2013, enjoys widespread support because it conveys some private land to the federal government as part of the trade off. But a local tribe of Native Americans opposes it, saying the tradeoff would surrender sacred grounds to copper mining.