The latest push to neutralize the legislation comes on the heels of an earlier effort to repeal the law. That passed the House but fell short in the Senate.
The spending bill, needed to fund the government through the end of the fiscal year on Sept. 30, is being drafted by the House Appropriations Committee, which is seeking deep spending cuts. The current stop-gap bill expires March 4.
While the initial version isn't expected to include the health-law funding ban, Republicans plan to introduce it as an amendment to the bill, Mr. Cantor said. It is expected to block the use of money in the bill to carry out the law, for example by preventing the Department of Health and Human Services from hiring more workers to oversee the new benefits.
The House Republicans' strategy means President Barack Obama's health-care initiative will be a major hurdle to passing the government-wide spending bill. Democratic leaders in the Senate are unlikely to back any move to defund the new law.
With repeal of the health law dead for now, Republicans have also called for rolling back specific parts of the legislation, such as the requirement that most Americans carry health insurance or pay a fine.
That requirement has become politically sensitive for Democrats in swing states after two federal judges ruled it was unconstitutional. Lawmakers from both parties are calling for Congress to look into replacing the requirement.
At least two Senate Democrats who voted for the new health-care law—Nebraska Sen. Ben Nelson and Missouri Sen. Claire McCaskill—say they're looking at other ways to bring people into the insurance pool without mandating coverage.
Health-industry officials say one alternative would be to make insurance more expensive for those who wait before buying it—similar to an incentive in theMedicare program for the elderly. But Republicans may not come through with the votes for such a measure, given it could help Democrats salvage a law strongly opposed by the GOP.