(Bloomberg) — House Majority Leader Eric Cantor and other Republicans are shifting strategy in talks on avoiding a U.S. government shutdown, seeking to delay President Barack Obama’s Affordable Care Act as a part of fiscal talks.

The Republican priority “is first and foremost a delay of ‘Obamacare,’” Cantor of Virginia said on the House floor Thursday in Washington, the same day the legislative body also voted to ban new subsidies for people seeking insurance under the law until a verification system is enacted to confirm subsidies go to those in need.

Senate Majority Leader Harry Reid, a Nevada Democrat, immediately rejected the idea of a delay and said the House is on a track toward shutting down the government when the fiscal year ends Sept. 30. Reid said he told House Speaker John Boehner during a meeting today that efforts to meddle with the ACA were “a waste of time.” The subsidy bill that was passed in the House has little chance in Senate.

“Let’s stop these really juvenile political games,” Reid said.

Neither chamber has acted on legislation to finance the government for the 2014 fiscal year that starts Oct. 1. The U.S. government also is projected to reach its debt limit as early as mid-October. Reid repeated Democrats’ call for a debt-limit increase with no added policy changes.

House Republican leaders are trying to avert a government shutdown while satisfying caucus members who are willing to risk a financial crisis to sidetrack the health-care measure passed during Obama’s first term.

Vote delayed

Yesterday, Boehner and Cantor delayed a vote on a spending plan opposed by dozens of their Republican members. The measure sought to force the Senate to vote on defunding Obama’s ACA. Many members balked because the proposal would still have funded the government even if the Senate kept funding for the health care law.

Cantor told members today that the House may cancel a planned recess the week of Sept. 23 because of the negotiations on the spending measure.

Other House members are talking about voting for a delay in the health law instead of trying to defund it. Among them, Representative Mike Simpson, an Idaho Republican, said members are realizing that “we’re better off with a delay.” The talks are centered on how to “best” delay the law, he said.

Boehner and Reid met Thursday with House Minority Leader Nancy Pelosi, a California Democrat, and Senate Minority Leader Mitch McConnell, a Kentucky Republican to discuss financing the government and raising the debt ceiling.

‘Good fallback’

Representative Trey Gowdy, a South Carolina Republican, said delaying the ACA would be a “good fallback” for the House spending-bill plan.

The Republican Study Committee, a group of lawmakers that promotes small government, discussed demanding a one-year delay in the health law in exchange for increasing the debt limit. Ross said the postponement would produce savings that could be used to cancel some of the automatic federal spending cuts that started in March.

Another variation floated by Louisiana Republican John C. Fleming would be to undo this year’s automatic federal spending cuts in return for postponing the ACA a year.

The spending bill “is going to have to change,” Representative Thomas Massie, a Kentucky Republican, told reporters yesterday. He said he is among 50 to 80 Republicans who want to stop funding for the ACA and oppose their leaders’ plan.

‘Better place’

Republican Senator Johnny Isakson said today the stopgap spending bill is a “better place” than the debt limit for Republicans to wage their fight to postpone the health care law. Trading a postponement of the law for relief from the automatic spending cuts is a “possible” basis of a compromise he’d be willing to explore, Isakson said at a Bloomberg Government breakfast.

“There’s bipartisan interest in solving the sequester problem,” Isakson said. “There is not bipartisan interest in postponing ‘Obamacare,’” he added, saying that vote “would be problematic for a lot of Democrats” seeking re-election next year because many voters dislike the law.

Isakson predicted the continued partisan wrangling won’t lead to a government shutdown even as the Oct. 1 deadline nears.

Democratic opposition

Boehner and Cantor needed the bulk of their fellow Republicans to support their earlier spending plan because Democrats opposed it. Hoyer of Maryland said this week he was urging colleagues not to vote for it.

“The American people are witnessing yet another sign that Republicans can’t get their own act together, even when a government shutdown hangs in the balance,” Pelosi said in a statement yesterday.

Boehner said earlier this week his goal was to “cut spending and to stop Obamacare,” not to shut down the government.

“We’ve got some time left here and conversations are taking place,” Representative Hal Rogers of Kentucky, chairman of the Appropriations Committee, told reporters last week. “It’s not time to panic.”

The House has voted 40 times to repeal, delay or defund all or part of the health care law. The Senate has refused to take up almost all of those measures.

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