Did President Obama win or lose on the payroll tax cut?

On one hand, the Senate on Saturday voted to extend the tax holiday for 160 million Americans for two months. On the other hand, the legislation ignores two of the president’s core ideological demands.

For months, Obama had called on Congress to impose higher taxes on millionaires to pay for the tax cut, but the Senate bill instead raises fees on mortgages backed by federal insurers Freddie Mac and Fannie Mae.

And 10 days ago, the president expressly vowed to “reject” any legislation that tied the controversial Keystone XL oil sands pipeline to the payroll tax cut; the Senate bill requires the administration to decide on the project — currently under a federal environmental review scheduled to last another year — within two months.

Still, during a brief appearance in the White House briefing room, Obama read a statement in which he called the Senate’s action a victory for middle- and working-class Americans.

“I’m very pleased to see the work that the Senate has done,” Obama said. “While this agreement is for two months, it is my expectation — in fact it would be inexcusable for Congress not to further extend this middle-class tax cut for the rest of the year. It should be a formality.”

He took no questions from reporters.

Afterward, senior administration officials worked hard to spin the Senate’s action as a victory for the president despite the Keystone provision inserted into the legislation by Republican leaders.

“It is absolutely not a blink,” said one administration official, who like the others spoke on the condition of anonymity to discuss White House political strategy.

“Republicans were running around harrumphing that they would make [Obama] do the Keystone pipeline. All they did was shorten the review process,” the official said. “This does not make him do a single thing.”

Republicans would probably disagree.

To Obama’s GOP adversaries, the legislation, which heads to the House on Monday, will force the president into the awkward position of actively blocking the pipeline, which could create thousands of jobs and has been supported by labor unions, as well as some Democratic lawmakers.

The White House, which last month ordered the environmental review of Keystone after objections from environmental advocates, had not expected to make a decision until after the 2012 presidential election next November.

In a background briefing for reporters on Saturday, the senior administration officials pointed to a statement last week from the State Department, which is conducting the pipeline review, declaring that it would be unable to meet the accelerated timeline and, thus, unlikely to issue a permit for the Keystone project to proceed.

That means Republicans who favor the pipeline are driving it toward virtually certain defeat through their strategy of forcing the president’s hand, the officials said.

“Our core values are that ... we would not accept something that dictated the [approval] of Keystone,” one official said. “This does not do that.”

As for the millionaires’ surtax, which Obama has pushed for in a series of speeches across the country in support of his $447 billion American Jobs Act, the White House says now that the surtax was never a requirement for a payroll tax cut deal.

If a better idea emerged, officials said, the president was always open to entertaining it. And when Congress revisits the tax cut in February, when the current two-month extension is set to expire, the president will again put the surtax on the table, they added.

The White House is confident that Congress will be persuaded again to extend the popular payroll tax cut with the fall election season nearing.

The Obama advisers urged reporters to take a longer view when assessing the winners and losers of the current negotiations.

Republicans, they said, would not even be entertaining the payroll tax cut extension — as well as an extension of long-term unemployment insurance also contained in the Senate bill — were it not for the president’s public barnstorming tour.

“Every Republican in town knows they are in a boatload of trouble, caught between a tea party base whose priorities are way out of touch,” another administration official said. “They have repeatedly taken a series of positions that are the antithesis of what their voters want.”

That official added: “Some folks are playing chess, and some are playing checkers.”

So which side is playing chess, a reporter asked.

“We’ll see,” the official replied. “You guys can keep score.”