The House approved the measure to keep the government operating on a voice vote and sent it to the Senate. Spending authority is scheduled to run out after Wednesday.
The stop-gap continuing resolution is a joint resolution to provide bridge funding to government agencies and is needed because lawmakers didn't pass a 2014 budget bill by Sept. 30, 2013, the end of the government's last fiscal year.
The White House issued a statement supporting the House measure, saying the "legislation adheres to the funding levels agreed to in the Bipartisan Budget Act of 2013, and reflects compromise by both parties. It unwinds some of the damaging cuts caused by sequestration, ensures the continuation of critical services that the American people depend on, and invests in essential areas such as education, infrastructure, manufacturing, and scientific research, which contribute to growing the economy, creating jobs, and strengthening the middle class."
The White House also said the measure returns the budget process to "regular order" and urged swift passage.
If both chambers don't pass the continuing resolution by Wednesday, parts of the government could shut down as they did Oct. 1-16.
But congressional leaders promised they would avoid a shutdown replay, which furloughed some 800,000 federal employees and required another 1.3 million more to report to work without knowing when they'd get paid.
House and Senate leaders said they expected, after passing the continuing resolution, to move quickly to the trillion-dollar omnibus bill -- which is actually 12 bills in one, totaling 1,582 pages -- with the intention of passing and sending it to President Obama by Saturday.
The compromise omnibus measure, unveiled Monday night, provides $1.012 trillion for discretionary spending for the fiscal year ending Sept. 30.
The money includes $520.5 billion for military programs and $491.7 billion for domestic programs.
The bill allocates an additional $92 billion for emergency overseas funding, such as for the war in Afghanistan and for aid to Syrian refugees, the Wall Street Journal said.
The spending plan is $1 billion less than when Obama took office in 2009. At that time it was $1.013 trillion, the Journal said.
Some conservative Republicans who campaigned in 2010 vowing never to vote on a phonebook-size bill they didn't have time to read were expected to vote against it because they'd have only three days to look it over, the New York Times said.
As a result, the bill will need bipartisan support to pass, the newspaper said.
But GOP and Democratic leaders said they believed they would easily get House and Senate majorities, even if they face loud protests from both the right and the left.
The omnibus measure reverses some cuts to military veterans' pensions that were included in a broader budget agreement last month and defeats Republican efforts to strip financing to carry out the Affordable Care Act.
"Obamacare lives another day," Senate Appropriations Committee Chairwoman Barbara Mikulski, D-Md., told reporters.
But the bill keeps funding for the agency implementing the 2010 healthcare law at last-year's levels and cuts $1 billion from a public-health fund Republicans said they feared the White House would use to bolster the law's online insurance exchanges.
The bill also restores some funding cut last year from domestic programs such as the National Institutes of Health and the Head Start Program, and it continues to let the Environmental Protection Agency regulate greenhouse gases and reverse clean water regulations.
At the same time, the legislation cuts $503 million from the Internal Revenue Service last-year budget, dropping it to $11.3 billion this year, and toughens requirements for the IRS to report its activities to the public and Congress after the agency's scrutiny of Tea Party groups seeking non-profit status.
No money is budgeted for some administration priorities conservatives opposed, such as construction of high-speed rail and a preschool development grants program.
On the other side, new regulations supported by liberals are blocked, including a standard for energy-efficient light bulbs and livestock and poultry controls.