They also, as expected, promised tea party lawmakers a chance to first use a routine temporary government funding bill to try to muscle the Democratic-controlled Senate into derailing President Barack Obama's health care law.
"That fight will continue as we negotiate the debt limit with the president and the Senate," said House Majority Leader Eric Cantor, R-Va.
Obama said again that he won't knuckle under to the GOP's demands
The GOP strategy appears to assume that the Senate will strip out the "defund 'Obamacare'" provision and send it back. The House would then face a choice: pass the measure without the health care provision or continue the battle and risk a partial government shutdown when the new budget year begins Oct. 1.
Speaking to CEOs of the Business Roundtable Wednesday, Obama called on the corporate leaders to use their influence to avoid a potentially damaging showdown over the debt ceiling. He reiterated his promise to not negotiate over the need to raise the nation's borrowing limit, which the government is expected to hit as early as next month.
He blamed "a faction" of the Republican Party for budget brinkmanship designed to undo his three-year-old health care law.
"You have never seen in the history of the United States the debt ceiling or the threat of not raising the debt ceiling being used to extort a president or a governing party and trying to force issues that have nothing to do with the budget and have nothing to do with the debt," Obama said.
"So I'm happy to negotiate with them around the budget, just as I've done in the past," he added. "What I will not do is to create a habit, a pattern, whereby the full faith and credit of the United States ends up being a bargaining chip to set policy. It's irresponsible. The last time we did this, in 2011, we had negative growth at a time when the recovery was just trying to take off."
GOP leaders telegraphed that they would likely concede to the Senate's demand for a stopgap spending bill shorn of the Obamacare provision — but that they would carry on with the fight on legislation to increase the government's borrowing cap.
"There should be no conversation about shutting the government down. That's not the goal here," Said House Speaker John Boehner, R-Ohio.
"I don't think that any reasonable person thinks there's anything to be gained by a government shutdown," said Sen. John Cornyn, R-Texas. "Rather than a shutdown of government, what we need is a Republican victory in 2014 so we can be in control. I'm not sure those are mutually compatible."
The latest strategy was presented to rank-and-file Republicans at a closed-door meeting Wednesday. GOP lawmakers and aides said it was received well.
It's a reversal from an earlier strategy, rejected last week by angry conservatives, that would have sent the measure to the Senate as two bills to ensure that the Democratic-controlled chamber would be able to ship the spending measure straight to the White House and more easily avert a government shutdown after the Sept. 30 end of the budget year.
The idea then was to avoid a subsequent vote on a "clean" stopgap spending bill in the House after Senate Democrats voted to strip out the provision. Stopgap funding bills are typically routine, with neither House nor Senate looking to use them to pick a fight.
There's some risk, however, that if the Senate were to send the measure back, angry GOP conservatives might be looking for a fight and could withhold their votes rather than surrender to the Senate and its top Democrat, Majority Leader Harry Reid of Nevada.
The latest move attempts to shift the battle to must-pass legislation to raise the government's $16.7 trillion borrowing cap on their own terms by pairing it with a roster of conservative priorities, including a renewed assault on the health care law and a mandate to build the Keystone XL pipeline.
"In the coming week, we will unveil a plan to extend our nation's ability to borrow while delaying Obamacare," Cantor said. "Those discussions will also focus on a path forward on tax reform and the Keystone pipeline."
Conservatives want to take a must-pass bill hostage and add the assault on the Affordable Care Act in an attempt to force Obama and congressional Democrats to make concessions. GOP leaders have viewed the effort with skepticism since Democrats would never go along.
The idea of defunding Obama's health care law has been a goal of tea party conservatives such as Sen. Ted Cruz, R-Texas, and outside groups like the Heritage Foundation.
Meanwhile, a large group of House conservatives intends to unveil legislation providing an expanded tax break for consumers who purchase their own health coverage and increasing the government funding for high-risk pools, according to lawmakers who said the plan marked the Republicans' first comprehensive alternative to Obama's health care overhaul.
Conservatives are frustrated that Republicans control only one chamber of Congress and have little chance to enact their agenda over the opposition of Obama and Senate Democrats.
Also Wednesday, White House budget office director Sylvia Burwell sent agencies a memo to guide them in their planning in the event of a lapse in funding authority on Oct. 1. As in prior shutdowns, many agency programs would continue.
A shutdown impasse would leave the government without funding authority to pay its workers, including the military, or enter into new contracts until a bill is passed. But essential programs like the military, air traffic control, food inspection, disaster relief and firefighting would continue to function since they're related to protecting life and property. So-called mandatory programs like Social Security and Medicare, which are funded as if on autopilot, would also continue.
National parks would mostly close, most passport applications could not be processed and the space program would largely be put on hold, among other results.
A top House Democrat, Rep. Steny Hoyer of Maryland, said Tuesday he would not support the stopgap funding bill under any circumstance since it would fund programs at an annualized funding rate of $986 billion, a level consistent with automatic, across-the-board spending cuts known as sequestration that Democrats are trying to reverse.
But if the Democratic Senate goes along with that funding level, as insiders have signaled, and if Obama endorses the straightforward funding measure, House Democrats likely could be counted upon to provide the votes. The question is whether GOP leaders would want to pass the measure with help from Democrats, which Boehner did on several occasions earlier this year to the consternation of conservatives.
Associated Press writer Jim Kuhnhenn contributed to this report.
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