The United States has a jobs problem and there's not a lot President Barack Obama or Federal Reserve Chairman Ben Bernanke can do about it.

In the face of rising risks of a recession that could imperil his re-election chances next year, Democrat Obama wants Congress to extend a payroll tax cut and emergency unemployment benefits that are due to expire in December.

But the Republican-controlled House of Representatives is emboldened by budget concessions it made Obama swallow to lift the country's debt limit this week and he has little political leverage to win significant fresh spending to aid growth.

Obama does not have much presidential persuasion left. He is running out of capital, said James Thurber, of American University's Center for Congressional and Presidential Studies.

Obama's political opponents have been openly scornful of the impact of two previous stimulus packages, which were accompanied by extraordinary measures by the Federal Reserve to kick-start the U.S. economy.

It seems we've thrown everything at it. We've had QE1 and QE2, Stimulus 1 and Stimulus 2, and the unemployment rate is still 9.2 percent, said John Makin, an economist at the American Enterprise Institute in Washington. Maybe there are just not many options here at this point, he said.

World stock markets shuddered after disappointing U.S. growth and manufacturing numbers and investors rushed to buy long-dated U.S. Treasury bonds in a move that suggests deep concerns about the economic outlook.

Data on Friday is expected to confirm the U.S. unemployment rate remained stuck at 9.2 percent in July.

Lawrence Summers, a top Obama adviser until last year, wrote in a Reuters column on Tuesday the odds of another U.S. recession were 1 in 3. Goldman Sachs has said a slight tick up in the unemployment rate could provide a strong recession signal.

HARD-WON COMPROMISE

Obama signed a hard-won compromise on Tuesday to raise the $14.3 trillion U.S. debt limit in return for measures that will reduce deficits by at least $2.1 trillion over 10 years.

Joel Prakken of the forecasting firm Macroeconomic Advisers estimates an extension of the payroll tax cut could add about 0.25 percentage points to U.S. growth next year.

Republicans fought hard to cut spending but are open to tax cuts, and the White House expects bipartisan support when Obama advances the idea in the coming months.

But analysts are skeptical it will make much difference for an economy that is having trouble gaining traction.

A major option is extending the payroll tax cut. We did that in December, and the economy grew at a 0.6 percent annual rate over the first half of the year, said Makin.

But the economic benefit of extending the payroll tax cut will be curbed by the government spending cuts agreed to Obama, and a weak economy will make hitting deficit-reduction targets that much more difficult.

JPMorgan's Michael Feroli estimates fiscal policy will subtract about 1-3/4 percentage points from growth next year as spending cuts kick in, if the earlier payroll tax cut and unemployment insurance extensions expire on schedule.

Given that GDP growth has been 1.6 percent over the past four quarters when fiscal policy has been much less of a drag, this doesn't bode well for next year, he said.

JPMorgan has cut its first half 2012 growth forecast to 2 percent from 2.5 pct due to fiscal drag.

Bernanke also seems to have few options at his disposal.

The Fed is not expected to announce an extension of its so-called quantitative easing, or QE, measures to stimulate economic activity at a policy meeting on Tuesday, despite the sense of gloom descending on the economy.

If push comes to shove, the Fed would likely look to cement its promise of keeping in place a loose monetary policy for a long period. It might even consider shifting the composition of its Treasury note holdings toward longer maturities, an option Bernanke has raised as a way to give the economy some relief.

Someone should do something. Given that the Congress has declared itself unwilling to provide support for the economy, the Fed will feel pressure to try to do what it can, said Barry Eichengreen, an economics professor at the University of California, Berkeley.

NO GAME-CHANGER

However, the Fed's options hardly add up to a game-changing play to dramatically improve the U.S. outlook.

Everyone is really looking to the Fed to support the economy, and I think (Bernanke) would realize that you could only do so much with monetary policy, said Mike Knebel at Portland, Oregon-based Ferguson Wellman Capital Management.

The Fed's scope for more easing of monetary policy has been narrowed by a rise in core inflation, which bottomed at 0.9 percent in December but has since hit 1.3 percent.

As Obama signed the debt deal, which averted a devastating default and reduced the risk to the country's AAA credit rating, he promised more ideas to boost hiring soon.

The White House declined to say what he had in mind or when he would lay out suggestions. But Treasury Secretary Timothy Geithner said in an opinion piece in the Washington Post that Congress could make space to fund a payroll tax cut extension by locking in long-term budget savings.

With lawmakers out of town for a summer recess, no major initiative is likely before September, although Obama does plan a Midwestern bus tour from August 15 to August 17 to talk up jobs.

When it comes, the odds favor small steps that allow Obama to show he is taking action, without disturbing investors.

There is a good case to be made for additional stimulus, but given our fiscal situation it has to be targeted to create more jobs, said Karen Dynan, a scholar at the Brookings Institution in Washington.

(Additional reporting by Ann Saphir in Chicago and Tim Reid in Washington; Writing by Alister Bull; editing by Vicki Allen and Christopher Wilson)

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