WASHINGTON – House Republicans are pursuing an all-of-the-above strategy to halting President Obama’s healthcare law, using the threat of next week’s government shutdown and the need to raise the debt limit in mid-October as leverage in back-to-back high-stakes showdowns with the White House.

With the collapse of the GOP strategy in the Senate to stop the Affordable Care Act, the debate shifted Thursday to the House, where Republicans emerged from a closed-door strategy meeting with their commitment to fight the health law undiminished.

Speaker John A. Boehner (R-Ohio) promised to link a one-year delay of the healthcare law to the administration’s request to raise the debt limit by Oct. 17, opening a new front as Republicans hunkered down for a weekend of brinkmanship that could shut down the government by Tuesday.

“The president says, ‘I'm not going to negotiate,’” Boehner said afterward. “Well, I'm sorry, but it just doesn't work that way.”

Boehner’s two-pronged strategy serves several purposes. By pushing the debt legislation forward, he is giving his restless right flank a new battleground in their efforts to stop Obamacare that could lower the temperature this weekend as the House must pass legislation to continue to fund the government or risk being blamed for a shutdown.

But by keeping the shutdown threat on the table, Boehner gives his Republicans the chance to bounce the government-funding bill back to the Senate later this weekend, just hours before government offices could close, with other provisions designed to chisel away at the Affordable Care Act.

The Senate agreed late Wednesday to speed up the schedule for voting on the government funding bill by one day after Sen. Ted Cruz (R-Texas) failed to rally fellow Republicans against it. The next key Senate vote will be Friday, with final passage expected no later than Saturday.

The shutdown bill then goes to the House, where Boehner may tack on other Obamacare provisions, including a repeal of a medical device tax, an end to federal employer subsidies for healthcare for some federal workers, or a delay of the requirement that all Americans carry insurance, or face a fine, starting in 2014.

But none of the Republican approaches offers a clear exit strategy, as Democrats in the Senate are expected to reject any effort to dismantle the president’s signature healthcare law.

Even Boehner’s turn to debt-limit legislation remained a work in progress, as drafting the bill has become complicated by the long list of extra measures that GOP leaders are adding to gain support from reluctant Republicans.

Treasury Secretary Jacob J. Lew warned that failing to raise the $16.7-trillion debt limit to continue paying the nation’s bill would be “catastrophic,” leading to a possible rare debt default.

But Republicans are loading up the debt bill with demands that the administration approve construction of the stalled Keystone XL oil pipeline between Canada and the United States, end several environmental regulations and other provisions.

Lawmakers appeared resigned to a long weekend – and fall – of budget battles.

“I’m ordering pumpkins,” said Rep. Greg Walden (R-Ore.) as he left the private session, “and turkeys and Christmas trees.”

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lisa.mascaro@latimes.com

Twitter: @LisaMascaroinDC