The Senate’s New Year’s Eve compromise on the “fiscal cliff” hit major turbulence in the House on Tuesday, and the Republican majority is likely to try to amend the bill and send it back to the Senate, House Republicans said.

House Majority Leader Eric Cantor (R-Va.) told his conference he is flatly opposed to the Senate bill without more spending cuts, members said as they emerged from a nearly two-hour Republican meeting in the Capitol.

According to sources in the room, Cantor said that he did not “support” the Senate-backed bill but stopped short of saying he would vote against it if the House took it up on the floor.

The sizeable objections among House Republicans to the Senate approach risks scuttling the deal worked out by Senate Minority Leader Mitch McConnell (R-Ky.) and Vice President Biden on Monday. That deal passed early Tuesday in the Senate by 89 to 8 votes.