Correction: An earlier version of the story incorrectly identified Sen. Ted Cruz (R-Tex.) as a House member. This version has been corrected.

Budget expert Stan Collender, author of "The Guide to the Federal Budget," explains why he's certain that the government will shut down next week. (The Washington Post)

With federal agencies set to close their doors in five days, House Republicans began exploring a potential detour on the path to a shutdown: shifting the fight over President Obama’s health-care law to a separate bill that would raise the nation's debt limit.

If it works, the strategy could clear the way for the House to approve a simple measure to keep the government open into the new fiscal year, which will begin Tuesday, without hotly contested provisions to defund the Affordable Care Act.

But it would set the stage for an even more nerve-racking deadline on Oct. 17, with conservatives using the threat of the nation’s first default on its debt to force the president to accept a one-year delay of the health-care law’s mandates, taxes and benefits.

President Obama warned Thursday that he will not accept delays to the program’s taxes, mandates and benefits. He said Republicans “have just spun themselves up over this issue.”

“The closer we’ve gotten to this date, the more irresponsible people opposed to this law have become,” Obama said at Prince George’s Community College in Largo, Md., referring to the Oct. 1 start of enrollment in the program’s new health-insurance plans.

Countdown to the (possible) shutdown

“The Affordable Care Act is here to stay,” Obama said, stressing that he would not negotiate delays or other changes to the law as part of budget talks or the debt-ceiling process.

Thursday morning, House Speaker John A. Boehner (R-Ohio) refused to outline what Republicans would attach to the spending bill, formally known as a continuing resolution, when it arrives from the Senate.

“We’re not going to have a discussion about the CR — speculate about the CR — until the Senate sends us their bill,” he told reporters.

Two hours after Boehner’s announcement, Senate Majority Leader Harry M. Reid (D-Nev.) said the Senate would not accept another House-passed funding resolution with different legislative strings attached to it.

“They keep digging, deeper and deeper,” Reid told reporters as a countdown clock ticked away the days, hours, minutes and seconds to Monday night’s shutdown deadline.

Sen. Barbara Mikulski (D-Md.), chairman of the Appropriations Committee, rejected any proposal to rein in Obamacare in either the government funding bill or the debt ceiling. “You can huff, you can puff for 21 hours, but you cannot blow the Affordable Care Act away,” she said, referring to a filibuster-like anti-Obamacare speech by conservative Sen. Ted Cruz (R-Tex.) that began Tuesday afternoon and ended Wednesday.

At their weekly closed-door meeting with rank-and-file Republicans, Boehner and his lieutenants outlined the plan to raise the debt limit. If it wins approval, the leaders hope to introduce the debt-limit bill later Thursday and hold a vote as soon as Saturday — letting GOP lawmakers mount a fresh assault on the health-care law before deciding whether to shut down the government.

The debt-limit bill will be loaded with dozens of other conservative priorities, including the approval of the Keystone XL oil pipeline.

Rep. Steve Southerland (Fla.), who attended a Wednesday meeting on the strategy on behalf of the massive class of GOP lawmakers elected in 2010, sidestepped questions about whether conservatives would be willing to trade the leverage of a government shutdown for the leverage of a default.

Leaders are “running the traps on every conceivable formula,” he said. “We’re looking at every possibility.”

The strategizing in the House came as Senate Democrats advanced a slow but inevitable campaign to approve a measure to keep the government open without undermining the president’s most significant legislative achievement, commonly known as Obamacare.

After Cruz staged his 21-hour attack on the law, he joined all 99 of his Senate colleagues Wednesday in voting to end his filibuster and start debating a House-passed bill that would fund the government through Dec. 15.

As written, that measure also would defund Obamacare. But after a long debate expected to stretch into the weekend, Senate rules permit Majority Leader Reid to strip out the anti-Obamacare provisions, change the expiration date on the funding bill to Nov. 15, and pass the measure with a simple majority achieved entirely with Democratic votes.

With passage of the funding bill all but certain, Cruz’s talk­athon accomplished little. The Senate is expected to approve the bill Saturday. That would give Boehner barely 48 hours to pass the Senate version or respond with add-ons.

Among the options: Repeal a tax on medical devices that was adopted to help finance the health initiative but has never been popular in either party; abolish insurance subsidies that members of Congress and their staffs receive from their employer, the federal government; or even delay the health-care law’s requirement that every individual purchase insurance, known as the individual mandate.

But any move to change the bill in the House, no matter how noncontroversial, would require another vote in the Senate, virtually guaranteeing a shutdown. Both chambers must agree on a funding plan by midnight Monday to keep federal agencies open Tuesday.

That leaves approval of the Senate bill as Boehner’s best bet for avoiding a shutdown. And the evolving debt-limit bill could help.

The debt-limit measure, which was still being loaded with new provisions late Wednesday, amounts to a grand conservative wish list. In addition to delaying implementation of the health-care law for one year, the bill would establish a timetable for tax reform, squeeze $120 billion from federal health programs over the next decade — in part by tightening medical malpractice laws — and cut federal civil service pensions.

The measure also would approve construction of the Keystone XL oil pipeline and advance other GOP economic goals, including increasing offshore oil drilling, blocking federal regulation of greenhouse gas emissions and restricting most forms of federal industry regulation.

About the only major piece of the Republican agenda missing from the bill is a ban on late-term abortions — and some lawmakers who oppose abortion were arguing to add that, GOP aides said.

By stuffing the bill with so many appealing provisions, GOP leaders hoped to persuade at least 217 Republicans to support its sole negative aspect: raising the $16.7 trillion federal debt limit through Dec. 31, 2014 — an increase worth about $1.1 trillion, by independent estimates.

If the House passes the measure, GOP leaders could argue that it should become the new weapon for continuing the assault on Obamacare, allowing Republicans to abandon the fight against the government funding bill.

It was unclear late Wednesday whether that strategy would work. Rep. Pete Sessions (R-Tex.), a close Boehner ally, told reporters only that the debt legislation would be introduced “very soon.”

Meanwhile, White House officials scoffed at the strategy, with senior adviser Dan Pfeiffer tweeting that the plan “goes nowhere” and leaves Republicans “responsible for massive econ calamity.”

Added Simas, the White House political strategist: “What the American people will hear and see is that you have a minority within a party, and this is a minority within the Republican Party who are not listening to the more reasonable elements in the party, and they are willing to risk the full faith and credit of the United States of America and plunge the country into default because of their obsession with denying health insurance to 11 million Americans.”

As the standoff continued on Capitol Hill, White House officials were pressing ahead with the rollout of the health-care initiative, even as they played down expectations that huge numbers of Americans would sign up for insurance right away. As happened when Massachusetts implemented its universal coverage plan, Simas predicts that Americans will sign up in spurts mainly just before coverage begins in January, and again right before enrollment ends in March.

But enrollment will be up and running Tuesday even if the rest of the government shuts down, Simas said. Eighty-five percent of the Affordable Care Act’s funding comes from accounts that would not be affected by a shutdown.

Paul Kane contributed to this report.