The debt-ceiling deal that President Barack Obama hopes to negotiate with Republicans won't solve the nation's problem with red ink, as he stated in his first Twitter session with the public. And no, the payroll tax cut he got out of Congress isn't putting an extra $1,000 into the pockets of "almost every single American."

Obama took a few shortcuts with the facts Wednesday when fielding questions from people on the social networking site. Twitter's trademark brevity wasn't an issue with the president _ he answered verbally, for as long as he wanted. Even so, it was a juggling act and not everything came out right.

A look at some of Obama's claims and how they compare with the facts:

OBAMA: "My expectation is, is that over the next week to two weeks, that Congress, working with the White House, comes up with a deal that solves our deficit, solves our debt problems and makes sure that our full faith and credit is protected."

THE FACTS: The deal he seeks with Congress would, if reached, let the U.S. avoid defaulting on its debt payments. In that sense it would guard America's "full faith and credit," as the president said. But it would leave the underlying deficit and debt problems far from solved. Even Obama's proposal for $4 trillion in deficit cuts over 12 years would see the debt increase and leave the budget out of balance.

The bipartisan Committee for a Responsible Federal Budget estimates Obama's plan would require $7 trillion in borrowing over a decade.

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OBAMA: "I actually worked with Speaker (John) Boehner to pass a payroll tax cut in December that put an extra $1,000 in the pockets of almost every single American."

THE FACTS: Obama, who said at another point that the $1,000 went to "every American," misstated the reach and size of the payroll tax cut. By the White House's own calculations, 159 million Americans are benefiting from the tax cut. The U.S. population is more than 311 million. The White House says the cut is worth $1,000 to a "typical family" _ one making $50,000 a year. That's a far cry from $1,000 into the pocket of every or nearly every American.

The cut, which runs through this year, reduces the payroll taxes that workers pay on their wages to 4.2 percent from 6.2 percent. So a family making $40,000, for example, saves $800.

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OBAMA: "But if we had a goal where we're just reducing our dependence on oil each year in a staggered set of steps, it would save consumers in their pocketbook; it would make our businesses more efficient and less subject to the whims of the spot oil market; it would make us less vulnerable to the kinds of disruptions that have occurred because of what happened in the Middle East this spring; and it would drastically cut down on our carbon resources."

THE FACTS: Obama, his predecessors in office back to Richard Nixon and leaders in both parties have called for energy independence, an achievement that most energy experts consider pie in the sky. But Obama's latest remarks were a reality check of sorts. He spoke of reducing that dependence in steps, not ending it anytime soon, and conceded oil will remain central to U.S. needs.

History also supports Obama's statement that "we have not had a serious energy policy for decades. Every president talks about it; we don't get it done."

He no doubt meant that reducing energy dependence would cut carbon emissions, not resources.

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Associated Press writers Jim Kuhnhenn and Nancy Benac contributed to this report.