Faced with a House Republican bill that extends the payroll-tax holiday but does not raise taxes on millionaires, President Obama and Senate Democrats on Wednesday considered financing the extension with budget cuts, not the so-called “millionaire’s surtax.”

Meanwhile, House Republicans prepared an end-run around the effort by Senate Majority Leader Harry Reid, D-Nev., to stall passage of a massive, almost $1 trillion spending package so that Democrats can negotiate a more favorable payroll-tax cut deal.

White House communications director Dan Pfeiffer on Wednesday night reiterated in a statement the administration’s calls for passage of another short-term funding measure, “so that all parties have an appropriate opportunity to consider and complete all of the critical budget and economic issues necessary to finish our responsibilities for the year.”

Those were the biggest developments in a day characterized by little actual legislative movement but defined by hours of strategizing in the inner sanctums of leadership offices and House and Senate cloakrooms. All this occurred against a backdrop of a potential but unlikely government shutdown on Friday; a push for expedited consideration of the Keystone XL pipeline from Canada to the Gulf of Mexico; efforts to extend federal unemployment insurance; and a looming 27-percent pay cut for doctors who see Medicare patients. All of these remained in limbo while party strategists and the White House struggled to first conceive and then execute a bipartisan resolution—something congressional leaders took their first real step toward on Wednesday evening when they actually met with each other.

Reid, House Speaker John Boehner, R-Ohio, and Senate Minority Leader Mitch McConnell, R-Ky., met late on Wednesday in the first direct negotiations of the year-end stalemate, but how and when they would broker a final deal remained murky.

In other developments:

• House Republican leaders prepared to file a stand-alone spending bill that includes all the agreements reached with Democrats on the nine pending appropriations bills during conference committee. By bringing it to the floor as a separate bill, they seize Reid’s leverage on the payroll-tax cut package. He has Democratic conferees refusing to sign the conference report, thereby preventing it from coming to the floor, in an effort to extract more from the GOP on the payroll measure. Now the new bill could come to the House floor as early as Friday.

• House Budget Chairman Paul Ryan, R-Wis., prepared to unveil on Thursday a new way to overhaul Medicare that would greatly reduce the savings he originally proposed. Ryan’s new approach, negotiated with Sen. Ron Wyden, D-Ore., would retain a premium-support system where seniors receive a lump sum from the government to purchase private insurance. Unlike Ryan’s earlier proposal, the new premium amount would track actual Medicare price increases. This would shield seniors from benefit cuts but save far less money. Ryan’s original plan tied the amount of direct subsidies to the national inflation rate, even if medical inflation were to run far higher.

• On the payroll-tax debate, the Democrats’ shift in strategy reflected calculations that the Senate cannot extend the tax holiday by raising taxes, even on the small number of Americans who earn more than $1 million a year. Instead, Reid and Obama are turning to a combination of spending cuts and other revenue sources.

Among the options under serious consideration: reducing support for mortgage giants Fannie Mae and Freddie Mac, or raising the fees the government-sponsored enterprises charge lenders to guarantee mortgages; reducing farm subsidies; and selling broadband-spectrum access. The House-passed bill includes these and other spending cuts to finance a one-year extension of the payroll-tax cut and an extension of jobless benefits up to 59 weeks—40 weeks shorter than the current 99-week limit.

“They are exploring other offsets and could make a new offer with no millionaire’s surtax at all,” said a senior Senate Democratic aide.

White House press secretary Jay Carney hinted at the shift earlier on Wednesday as Obama flew to Fort Bragg, N.C., to recognize troops returning from Iraq.

“I don’t know what the endgame will look like,” Carney said. “Democrats, Republicans, the president all support … extending the existing payroll-tax cut to 160 million Americans for 2012.  They should pass a bill that does that—that pays for it in a fair way.”

Obama summoned Reid and his party leaders to the White House for a closed-door strategy session. Passage of the House bill appeared to increase pressure on Reid to find an alternative to the millionaire’s surtax. Democrats may have calculated that they had inflicted all the political damage possible on Republicans.

It was unclear when Senate Democrats would unveil their payroll-tax cut alternative.

Senate Republicans, who on Monday and Tuesday called for swift consideration of the House bill, on Wednesday reverted to a stalling strategy and refused to hold a vote they knew they would lose. The GOP fear is that voting on the House bill would give Reid a procedural advantage because he can hold that bill in his pocket and pour it into a final negotiated compromise.

“The onus falls on the majority leader of the Senate to actually do his work,” said House Majority Leader Eric Cantor, R-Va., after a meeting with other House GOP leaders.

Boehner added: “I’m tired of hearing what the Senate can’t do.”

While congressional leaders took jabs at each other’s maneuvers, the White House continued complaining about inclusion of controversial policy riders in the House GOP’s payroll-tax cut package.

Carney called the Keystone pipeline issue “extraneous,” but in no way indicated it would be a deal-breaker. Republicans want Obama to agree on a 60-day procedure to approve or reject the project. Obama had delayed a final decision on Keystone until 2013. Republicans and some Democrats, such as Sen. Kent Conrad of North Dakota, want a decision sooner.