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The proposal still does not meet President Trump's request for $5.7 billion to help build a wall on the U.S.-Mexico border.
The legislation would fund the Department of Homeland Security through Sept. 30, the end of the fiscal year.
Lawmakers are racing against a Friday midnight deadline for passage.
The Senate and House of Representatives aimed to pass the legislation later on Thursday, according to Reuters.
Then it is up to Trump to review and sign it into law.
The final version of legislation would reportedly give the Trump administration $1.37 billion in new money to help build 55 miles of new physical barriers on the southwest border, far less than what Trump had been demanding.
There is always a chance that Trump will seek more funds for wall construction by declaring a national emergency.