Virginia Rep. Eric Cantor told reporters after a two-hour closed-door meeting Tuesday with his GOP lawmakers that he did not support the bill.
He said House leaders were looking for "the best path forward" and that no decisions had been made.
Outgoing South Florida Congressman Allen West also is not in favor of the bill.
"I reviewed the Senate-passed legislation, and as it stands I will not support it if brought to the House floor," he said in a statement.
He added, "Raising taxes in order to increase federal government spending is illogical, and disrespectful to all hard-working American families."
West said the day is coming "when principled pragmatic Constitutional Conservatives will be sought after to restore the American Republic, and we will answer the call."
The Senate passed the measure early Tuesday by a sweeping 89-8 vote. House passage of the measure would send it to President Barack Obama for his signature. The bill would increase taxes on family income exceeding $450,000 and delay across-the-board spending cuts for two months.
House GOP leaders were considering amending the measure and sending it back to the Senate, but that step could produce a deadlock.
The wptv.com web team contributed to this report