Senate leaders from both major parties announced a two-year budget deal a day before federal funding runs out.
The bill has angered Republican fiscal hawks who claim it would lead to a $1tn (£717bn) deficit while Democrats oppose it for not addressing immigration.
But Republican House Speaker Paul Ryan has said he believes it will pass.
"I think we will," Mr Ryan told radio host Hugh Hewitt. "This is a bipartisan bill. It's going to need bipartisan support. We are going to deliver our share of support."
Congress has to reach a deal before government funding runs out at midnight on Thursday, when a one-month spending bill is set to expire.
Congressman Mark Meadows, chairman of the conservative House Freedom Caucus, has called the plan "eye-popping and eyebrow-raising".
"We took an official position last night to say we can't support this," he told CNN on Thursday.
Failure to reach a spending agreement led to a three-day government shutdown last month.
What's in the bill?
White House legislative affairs director Marc Short said the package would increase spending by "just shy" of $300bn (£216bn).
The Washington Post puts the figure at half a trillion dollars.
The Senate bill, which has not yet been publicly unveiled, reportedly increases defence spending by $80bn in the first fiscal year and $85bn in the second.
Non-defence spending, such as a programme to provide health insurance for children, would reportedly increase by $63bn this year, and $68bn next year.