Obama, speaking to CEOs at a meeting of the Business Roundtable, said, "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."
He attributed the effort to a "small faction" within the Republican Party.
R. Bruce Josten, executive vice president of the Chamber of Commerce for government affairs, urged the House in a letter to "act promptly to pass a (bill) to fund the government and to raise the debt ceiling," and then to return to health care, tax reform and other issues.
Whatever its ultimate impact on Republican lawmakers, the letter stands as a counter to an aggressive campaign by tea party-aligned groups including the Senate Conservatives Fund, Heritage Action and the Club for Growth in recent weeks to generate support for legislation to defund the administration's health care overhaul.
Also on Wednesday, a large group of House conservatives proposed the Republicans' first comprehensive alternative to the health care overhaul. It would provide expanded tax breaks for consumers who purchase their own insurance and increase government funding for high-risk insurance pools.
Under that proposal by the Republican Study Committee, people who buy coverage approved for sale in their states could claim a deduction of $7,500 against their income and payroll taxes, regardless of the cost of the insurance. Families could deduct $20,000. The RSC claims a membership of 175 members, about three-quarters of the House Republican rank and file.
The bill's introduction comes at a time when party leaders have yet to advance any comprehensive alternative to the law Obama signed in 2010, though the GOP House has voted repeatedly to repeal all or part of it. The GOP pledged three years ago to "repeal and replace" the existing law, a promise Obama often notes with disdain.
The approach outlined Wednesday by Boehner and the GOP leadership team underscored how quickly tea party lawmakers have shifted their principal focus in the weeks since Cruz and Sen. Mike Lee of Utah as well as the outside groups began stressing the issue in TV ads.
The leadership's initial proposal for avoiding a partial government shutdown was to couple funding for federal programs with a requirement for the Senate to cast a vote on defunding the health care program, a requirement that could easily have been evaded.
Conservatives quickly rebelled against that approach, forcing Boehner and his lieutenants to regroup.
Even as they did, they sought to emphasize their commitment to cutting federal spending and curtailing the debt, two issues that have consistently united the fractious rank and file since Republicans took control of the House nearly three years ago.
"Not since the Korean War has the federal government reduced spending two years in a row. We aim to make that happen," said the Republican majority leader, Rep. Eric Cantor of Virginia.
Spending would be set at $986.3 billion for the fiscal year that begins Oct. 1, although that would be further reduced in January by a new round of across-the-board sequester cuts that would trim the level to $967 billion.
"There should be no conversation about shutting the government down. That's not the goal here," Boehner said.
Republicans paid a heavy political price two decades ago as the result of twin government shutdowns, at a time then-Speaker Newt Gingrich was insisting President Bill Clinton agree to cuts in Medicare, Medicaid and other popular programs.
Nor are Republicans eager to shoulder the blame for any market-shaking government default, which would probably occur if the Treasury could not continue to borrow funds to pay debts already incurred. Treasury Secretary Jack Lew has estimated that without action by Congress, that default will arrive in mid-October.