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NEW YORK (CNNMoney.com) -- President Bush on Wednesday signed the $170 billion economic stimulus package passed by Congress last week.

Bush, saying that Americans are "concerned about our economic future," said he believes the stimulus package will provide a "booster shot" for the economy.

The government hopes the measure, which will send most Americans tax rebate checks by May, will either prevent a recession or make one relatively brief.

The package also includes tax breaks for equipment purchases by businesses, as well as payments to disabled veterans and some senior citizens. The bipartisan measure moved through Congress at relative break-neck speed, going from initial discussions to enactment in less than four weeks.

The package will pay most individual taxpayers $600 and $1,200 for married taxpayers filing joint returns as long as they are below income caps of $75,000 for individuals and $150,000 for couples. There is also a $300 per child tax credit.

Those rebates will put about $120 billion in the hands of individuals in the hopes that they will spend it and boost a faltering U.S. economy.

But there have been other reports in recent weeks showing increasing signs that the U.S. economy has already slipped into a recession.

Earlier this month, the Labor Department reported a drop in U.S. payrolls in January. Other reports released this month have shown a decline in activity in the service sector as well as more weakness in the housing market.

Economists generally agree that the economy should see a boost from the rebate checks. But most also agree that the full impact will be less than the total value of the stimulus package.

That's because some are expected to save their rebates or use it to pay down credit cards or other debt instead of spending it. In addition, some consumers may spend their rebates on imported items - which would provide a more limited lift to the U.S. economy.

"My guess is that that of the $110 billion to $120 billion of tax rebates, about half will go to U.S. products and services," said David Wyss, chief economist for Standard & Poor's.

There are also questions about whether the stimulus will actually be the key to ending or preventing a recession.

Even many of those who believe the United States is already in a recession are forecasting that the economy is poised to pull out of the recession in the second half of this year - regardless of the stimulus package - thanks to several big interest rate cuts by the Federal Reserve since last September.

"I don't think this is too little, but it might be too late," said Jeoff Hall, the chief U.S. economist for Thomson Financial. "By the time you get the intended effect, you may not need anything."

Other economists believe the economy is falling into a much more severe recession than can be turned around by this type of tax cut.

"The problem is that after the impulse from stimulus dies, if you fail to jump start private sector growth, you have to have more stimulus or slog through a more serious downturn," said Jared Bernstein, an economist with the Economic Policy Institute, a progressive Washington think tank.

Treasury Secretary Henry Paulson has said he believes the stimulus package could lift U.S. employment by about 500,000 jobs. Paulson and Federal Reserve Chairman Ben Bernanke are set to appear before the Senate Banking Committee Thursday to talk about the economy.

But some economists argue the economic lift from the stimulus is too short-term to prompt businesses to bring on additional workers.

"Businesses don't change their hiring or investment habits for a one-check pony," said Rich Yamarone, director of economic research at Argus Research. "There's no overriding need to hire workers for anything more than a temporary basis."