A dramatic rally in the last hour of U.S. trading Tuesday pushed stock exchange traded funds into the green to cap a volatile session.

The major stock ETFs closed higher after Federal Reserve Chairman Ben Bernanke said the central bank is closely watching economic data and stands ready “to take further action as appropriate to promote a stronger economic recovery in a context of price stability.”

SPDR S&P 500 ETF (NYSEArca: SPY) was up about 2% heading into the closing bell. Late Tuesday, the Financial Times reported European Union finance ministers are looking at ways to coordinate a recapitalization of the region’s financial institutions.

Speaking in Washington before the Joint Economic Committee, the Fed chief said Congress shouldn’t cut spending sharply while the economy remains weak, the Associated Press reported.

Interest rates are extremely low, and the Fed has already gone through two rounds of quantitative easing. There are worries the central bank may end up pushing on a string.

“Monetary policy can be a powerful tool, but it is not a panacea for the problems currently faced by the U.S. economy,” Bernanke said Tuesday in prepared remarks. “Fostering healthy growth and job creation is a shared responsibility of all economic policymakers, in close cooperation with the private sector. Fiscal policy is of critical importance, as I have noted today, but a wide range of other policies–pertaining to labor markets, housing, trade, taxation, and regulation, for example–also have important roles to play.”

He also acknowledged the recent weakness in economic data as consumer sentiment and the housing market remain sluggish.

On the economic front, “two months ago we judged that there was about a 25% shot of a recession over the next year, a 50% chance of a ‘muddle-through’ outcome of between 1 and 3% growth and a 25% chance of trend growth or better,” said David Kelly, chief market strategist at JP Morgan Funds.  “At the start of October, this still seems to be the case.”

On Friday, investors will get market-moving employment data as September nonfarm payrolls cross the wires.

Kelly doesn’t think the Fed’s “Operation Twist” is a good idea. The central bank is shifting its portfolio into long-term government bonds in an effort to force down interest rates.

“Since the start of August, the Federal Reserve has tried to stimulate economic activity first by assuring investors that short-term interest rates wouldn’t rise until 2013 and second by making adjustments in its vast security holdings to try to reduce mortgage rates,” the strategist wrote in a weekly outlook.

“However, given the obviously record low levels of interest rates already, it is hard to see how lower rates would encourage any borrowing. Meanwhile, the Fed has succeeded in conveying two very damaging psychological messages, first, that they are very worried about short-term economic prospects, and second, that borrowers can take their time in taking advantage of current low interest rates,” he added.

Kelly is also worried about what deep spending cuts would do to the fragile economy as politicians in Washington can’t seem to find a compromise on the pace at which the deficit should come down.

“As things stand right now, assuming that the ‘super-committee’ fails to come to an agreement, there is the potential for the deficit to fall from 8.5% of GDP in fiscal 2011, (which ended last Friday) to just 6.2% in this fiscal year,” he wrote.  “The huge drop in aggregate demand which this implies would be due to the expiration of temporary tax breaks agreed to a year ago, combined with an end to the extra spending in the original Obama stimulus package and it is probably more severe than the economy can handle right now.”

Full disclosure: Tom Lydon’s clients own SPY.