UPDATE 2-W.House's Orszag: Outlook for US jobs improving

(Adds Orszag comment on deficits, background, byline)

By Alister Bull

WASHINGTON, April 8 (Reuters) - A top adviser to President Barack Obama said on Thursday a U.S. economic recovery was gathering steam, playing down fears of a double-dip recession and emphasizing prospects for stronger jobs growth ahead.

"Are there risk factors that we need to be monitoring? Sure. But there does seem to be now a growing sense of momentum which is exactly what we need," said Peter Orszag, director of the White House Office of Management and Budget.

This upbeat assessment was somewhat at odds with cautious remarks elsewhere on Thursday by the Federal Reserve. Fed Board Governor Daniel Tarullo said the relatively modest pace of the recovery and still-high unemployment would continue to warrant easy money policies by the U.S. central bank.

Orszag, Obama's powerful budget chief, also said U.S. deficits were too high and need to be brought down over time.

But he said a lack of other investment opportunities was driving investors into U.S. government bonds, helping hold down long-term interest rates and limiting risks of a problem with U.S. funding if foreign demand dried up over deficit concerns.

"Right now we have a collapse in private borrowing and there is not an immediate concern. But over time the projected deficits are too high. They need to come down and we absolutely must get ahead of that problem or else we are going to face an excruciating set of trade offs," he said.

Orszag acknowledged that jobs were still a weak spot and stressed tackling an unemployment rate lingering near 10 percent was the Obama administration's most pressing economic challenge.

"The labor market is lagging behind and unemployment is higher than anyone would want and it is going to take time for it to turn around," he said.

U.S. unemployment was unchanged at 9.7 percent in March but the economy created 162,000 new jobs, delivering the strongest employment performance in three years. Growth has also perked up, with output expanding at a 5.6 percent annualized pace in the fourth quarter of last year.

Orszag described three phases during an economic recovery, with productivity spurting forward first as firms boost output without increasing hiring, then hours worked and temporary employment improving, before employers finally boost payrolls.

"It appears ... that we may be moving into that third phase, which would be a very good development for Americans workers," he said.

This gave him confidence a controversial $787 billion stimulus package signed by Obama last year, criticized by opposition Republicans for adding to the deficit, was working.

"The purpose behind the Recovery Act was to create a jolt or a jump start that would start a self-propelling sense of momentum in the economy. And I think if you are just looking at current indicators, right now it ... is succeeding."

(Reporting by Alister Bull, editing by David Alexander and Chizu Nomiyama)