Representatives Jared Huffman, Ted Lieu, Zoe Lofgren, and Ami Bera are calling for immediate action on the benefit.
The current unemployment aid of $600 a week runs out at the end of the week. The new proposal calls for giving workers 70% of pre-pandemic wages.
"This $600 additional benefit that came under the CARES Act is being portrayed as some kind of windfall by Republicans, something that is allowing people to sit back and live a life of Riley and not go back to work, that is not reality," said Rep. Huffman.
The $600 weekly jobless benefits boost, which was approved as part of the March aid package, officially expires July 31, but because of the way states process unemployment payments, the cutoff was effectively Saturday.
Under the GOP proposal, the jobless boost would be reduced to $200 a week for two months and phased out to a new system that ensures no more than 70% of an employee's previous pay. States could request an additional two months, if needed, to make the transition.
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KGO-TV and the Associated Press contributed to this report.