Alexandria Ocasio-Cortez faces a primary challenge from former CNBC host Michelle Caruso-Cabrera.
Some Democrats fear a Bernie Sanders candidacy could spell trouble in tight Congressional races.
The measure was criticized by politicians concerned about the U.S.'s growing budget deficit.
The bills' extra provisions include extensions of tax breaks and the repeal of some taxes to fund Obamacare.
The House's impeachment focus may prevent the finalization of a trade deal between the U.S., Canada and Mexico.
The deal funds the government and averts a shutdown until Dec. 20.
Republicans plan to reduce the debt by repealing Obamacare, House Minority Leader Kevin McCarthy said.
The House speaker said a trade deal would be rejected if it threatens peace in Northern Ireland.
Trump once promised to eliminate the $22 trillion federal debt, but the deficit is approaching $1 trillion a year.
Nancy Pelosi faces one of the most politically challenging periods of her speakership.
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