The procedural vote was 68 to 13.
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Challenges remain, however, to prevent a shutdown as lawmakers race the clock ahead of a Friday deadline with little room for error.
Congressional leaders announced over the weekend that the short-term funding extension will set up two new funding deadlines on March 1 and March 8.
The extension will provide more time for full-year appropriations bills to be negotiated and passed.
In the Senate, a time agreement will still need to be reached to schedule a final passage vote before Friday.
If any senator objects, that could slow the process and threaten a shutdown.
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The House will also need to take up the measure and pass it once it is approved by the Senate.
Schumer emphasized on Tuesday that they will need full cooperation from parties in both chambers.
"If both sides continue to work in good faith, I'm hopeful that we can wrap up work on the CR no later than Thursday," he said, referring to the short-term funding extension.
"The key to finishing our work this week will be bipartisan cooperation in both chambers, you can't pass these bills without support from Republicans and Democrats in both the House and the Senate."
In the House, Speaker Mike Johnson faces an extremely narrow majority and is facing pushback from his right flank.
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Johnson has already faced fierce criticism from conservatives over a topline spending deal he struck with Schumer, which would set spending at close to $1.66 trillion overall. And conservatives were quick to criticize the proposal for a short-term funding extension after it was announced over the weekend.
"This is what surrender looks like," the far-right House Freedom Caucus posted on X.
Johnson has defended the topline agreement and said in a statement Sunday that the short-term spending bill "is required to complete what House Republicans are working hard to achieve: an end to governance by omnibus, meaningful policy wins, and better stewardship of American tax dollars."
In a rare event, lawmakers are confronting not one but two government shutdown deadlines early this year - on January 19 and February 2.
Congress passed stopgap legislation in November extending government funding until January 19 for priorities including military construction, veterans' affairs, transportation, housing and the Energy Department. The rest of the government is funded until February 2.