As of midweek last week, the strategy apparently won't include tying raising the $17 trillion debt limit to either approval of the Keystone pipeline or rolling back a portion of the Affordable Care Act, aka Obamacare.
Republicans also floated attaching language that would reverse changes to cost-of-living adjustments to the military, which, Politico noted, would have to be offset by another budget reduction measure.
House Republicans left Washington Thursday without a plan and without taking any action.
"Well I think that we're still looking for the pieces to this puzzle, but listen, we do not want to default on our debt and we're not going to default on our debt," House Speaker John Boehner said Thursday. "We're in discussions with members about how we can move ahead. We've got time to do this. We're going to continue to work at it. No decisions -have been made."
He made no bones about needing Democratic support for the bill, either, saying during a media availability there was broad support in his caucus, but I don't think we've got 218 votes for this."
Another question, the Hill said, is whether House Democrats can hold fast on their stance that the debt limit hike be a clean bill without concessions -- even modest ones -- to Republicans.
"We are urging the Republicans to pass a clean debt limit extension," Democratic Whip Steny Hoyer told reporters last week. "John Boehner has said, 'We believe that defaulting on our debt is the wrong thing. We don't want to do that.' We agree with John Boehner. It is the wrong thing. We don't want to do that."
Conservatives have said they would oppose a clean increase, but several told the Hill they were becoming resigned to seeing an unadorned bill sent to the Senate with Democratic help to reach 218, the minimum number of votes needed for passage.
"A clean debt-ceiling [bill] would not garner my vote, but if the House leadership chooses to go that route and believes that's in the best interests of the country and they don't need my vote to accomplish that, I'm OK with that," Rep. Cynthia Lummis, R-Wyo., said.
The borrowing cap, which was suspended as part of the agreement that ended the partial government shutdown last fall, went back into effect Friday.
Treasury Secretary Jack Lew, in a speech at the Bipartisan Policy Center, warned extraordinary measures likely will only allow the government to avoid a default until the end February if Congress fails to act.
"In February, the same large trust fund investments that were deferred last year are not available, and at the beginning of tax filing season, tax refunds result in net cash outflows that deplete borrowing capacity very quickly," Lew said. "We now forecast that we are likely to exhaust these measures by the end of this month."
Bottom-lining it, Lew said, "Time is short. Congress needs to act to extend the nation's borrowing authority, and it needs to act now."
At the White House, spokesman Jay Carney said something must be worked out in Congress.
"We certainly believe Republican leaders who say that we have to raise the debt ceiling. It's the responsibility of Congress to ensure that bills that have already been incurred are paid in a timely fashion so that the United States doesn't default," Carney said Thursday. "Our position, the president's position is what it has been for a long time, which is that we are not going to pay ransom in return for Congress fulfilling this basic responsibility."
During his remarks, Lew also threw water on an argument made last fall that President Obama could act on the debt ceiling.
"It is important to remember that increasing the debt limit is Congress's responsibility, and Congress' alone," he said. "That is because only Congress has the power to extend the nation's borrowing authority."
Boehner and other top House Republicans say they don't intend to push the debt limit battle with the Senate so far that a default looms.
Boehner said there were lots of opinions about how to address the debt limit debate, but "no decisions have been made."
Last fall, Republicans tied funding the federal government to the repeal of Obamacare and failed. The government partially shuttered for a couple of weeks in October and congressional Republicans got egg on their faces and took a bad hit in the public opinion polls.
This time, if polls are any indication, the American public won't be quite so kind.
A CNN/Opinion Research poll released last week indicated 54 percent of Americans would blame Republicans if a deal isn't reached, while just 29 percent would blame President Obama. Twelve percent said both sides would share the blame equally. The poll interviewed 1,010 adults across the country Jan. 31-Feb. 2 and has a margin of error of 3 percentage points.
It's as if the Senate and House are engaged in castle intrigue while attending a royal masque.
In a closed-door meeting Tuesday, Boehner urged Republicans not to be wedded to a position that has no chance of passing the Democratic-controlled Senate, one participant told Politico. He told his members the House must find "consensus" or the Senate will dictate terms of a debt limit increase and could send either a clean debt limit or something "worse."
Politico said Republicans are concerned the Senate would include in the debt limit some provision that Republicans oppose, such as extended unemployment benefits, which began expiring in December.
During a media availability last week, Senate Majority Leader Harry Reid said the upper chamber "will not play games with the full faith and credit of our country. ... We're not gonna pay ransom for a bill that Republicans supported for decades."
With the possibility of taking over the upper chamber come November, Republicans have not signed on to making demands in exchange for increasing the debt limit, the National Journal reported.
"Here's the reality -- and that is that we were badly burned by the shutdown of the government," Sen. John McCain, R-Ariz., said. "If it hadn't have been for Obamacare coming to the fore, it would have had even more impact. So Republicans are nervous about another showdown."
Still, Senate Democrats have expressed skepticism about the apparent Republican acknowledgement that a clean debt limit bill may be the only route available to them, particularly after Senate Minority Leader Mitch McConnell, R-Ky., called for attaching a spending cut and House leaders' saying a clean bill couldn't pass their chamber, the Journal said.
"The last thing we need to do with a fragile recovery is rattle sabers about debt ceilings and whether we're going to extend the debt ceiling," said Sen. Heidi Heitkamp, D-N.D. "We saw that that didn't work last time."
And Democrats on the tax-writing House Ways and Means Committee sent Boehner a letter noting the Treasury Department won't be able to pay out tax refunds without a higher debt limit.
In the letter, the Democrats noted the October government shutdown delayed the start of tax season until Jan. 31 and 110 million taxpayers, on average, received tax refunds averaging $2,700 last year, with nearly half of those refunds claimed by March 1.
Absent an increase in the debt ceiling, tax refunds can only be paid as money is received.
"Failure to act quickly will endanger our economic recovery and send a signal to American taxpayers that their refunds may be in jeopardy, potentially raising unnecessary panic among families awaiting their tax refunds," the 16 Democrats said in their letter.
The Campaign to Fix the Debt also urged Congress to work with the president to raise the debt ceiling in a responsible and timely manner.
"Our leaders cannot afford to play games with the full faith and credit of the U.S. government," said the organization's co-chairmen, former Sen. Judd Gregg, R-Neb., former Pennsylvania Gov. Edward Rendell, a Democrat, and former New York Mayor Michael Bloomberg, an Independent.
"At the same time, we must recognize that our long-term debt problems are still far from solved, and the debt ceiling vote should be viewed as a reminder that we still need to take steps to improve the country's fiscal outlook," the statement said, urging lawmakers and the president to pursue tax and entitlement reforms. "Congress and the president should embark on this process as quickly as possible."