But many Democrats, including House Minority Leader Nancy Pelosi (Calif.), are hesitant to support the bill because it doesn't include a path to citizenship for young undocumented immigrants, also known as DREAMers.
Without that, "this package does not have my support nor does it have the support of large numbers of members of our caucus", she said. "Without a commitment from Speaker Ryan comparable to the commitment from Leader McConnell, this package does not have my support".
The Democratic leader has dropped his push to use the budget talks to extract concessions on immigration from Republicans, leaving aside threats to shut down the government over the issue.
McConnell has promised Democrats he would allow a free-flowing Senate debate on immigration by February 8 and that he would not try to influence the outcome.
The deal would lift spending caps on U.S. defence and domestic programmes by about $300bn, AP news agency said this week.
The prospect of a ballooning budget deficit in the United States is one issue weighing on market sentiment this week.
But Sen. Rand Paul is holding up a vote on the Senate budget deal, accusing Republicans and Democrats of "spending us into oblivion". The incremental bills have given lawmakers more time to reach a deal, but negotiators have yet to reach a consensus on top-line spending levels that would satisfy both parties' demands - increased military spending for Republicans, and an equal increase in domestic spending for Democrats - and fund the federal government for longer than weeks at a time.
Chuck Schumer, the leader of the Senate Democrats, said the deal should break the cycle of partisan fights over spending. Pelosi and other Democrats blasted that GOP proposal as a ruse to slash funding for domestic programs.
Unfortunately for the Senate leaders, the deal faces opposition in the House. Freedom Caucus chairman Rep. Mark Meadows, R-N.C., called the bipartisan agreement a "Christmas tree of spending" on MSNBC Wednesday afternoon.
House Minority Leader Nancy Pelosi said the Democrats demand a commitment on bipartisan legislation to protect people who were brought to the USA illegally as children.
The House Bill does not contain changes to USA immigration law, which were a key point of contention in a partisan stand-off that led to a three-day partial shutdown last month.
Secretary of Defense James Mattis told reporters at the White House that he's optimistic that Congress will give the Pentagon the funding it needs.
What is President Trump's policy on DREAMers?