President Obama plans to sign his landmark economic recovery package Tuesday, but lawmakers are increasingly concerned that one of the bill's central proposals -- the tax cut for individuals -- will be too small and too temporary to have much effect. 

The stimulus plan would give a $400 tax cut to individuals and an $800 cut to couples. That boils down to an extra $13 a week for most workers starting in June. It would fall to about $8 extra per week next January. 

Some worry the cut is not enough to encourage consumers to go out and spend. And since two-thirds of the economy is consumer spending, the effectiveness of the tax cut in spurring workers to open their wallets is key to an economic revival. 

"The average person will get $8 per week in their paycheck and they will pass on to their grandkids $1.1 trillion in debt," said Republican Sen. Lindsey Graham, S.C. "We created more new government than we did jobs and the substance and process cannot repeat itself." 

Moody's economist Mark Zandi also says the nature of the tax cut could reduce the number of jobs created by the $787 billion stimulus package. 

"With regard to how much of the tax cut's going to spent for individuals, the White House, I think, is assuming that people are going to behave as if that tax cut is permanent, and I doubt that will be the case," he said. 

Zandi disputes White House estimates that the package will save or create 3 to 4 million jobs. He thinks the package will add 2 to 2.5 million jobs by the end of 2010. 

However, Democrats argue that their tax cut is a far more effective stimulus than the cut under former President Bush last spring, which gave taxpayers a lump-sum refund. 

"Instead of giving one paycheck at once, which George Bush did, and it really didn't stimulate the economy, the economists said 'stretch it out and people are more likely to put it into economy and get our economy going'," said Democratic Sen. Charles Schumer, N.Y. 

The rebates under President Bush were higher-- $600 per person and $1,200 per family, plus $300 dollars per child. But analysts say most taxpayers took the lump-sum rebate and either saved it or paid down debt. 

Economists say that is because they knew the money wasn't a permanent part of their family budgets and decided it was not sufficient to make any major purchases. 

Obama originally wanted a $500 tax cut for individuals and a $1,000 cut for couples in his package, but that got trimmed during negotiations in Congress 

So will $8 dollars a week unleash any more spending than the lump sum taxpayers received last year? 

One factor that could also affect job creation is the extent to which the stimulus helps small businesses, which create about three-quarters of all new jobs. 

"The tax provisions in the final compromise were gutted when it comes to business," Graham said. 

He complained that a tax benefit for business was cut from $67 billion to only $4 billion. 

Republican Rep. Peter King, N.Y., said others who do little to create jobs get far better treatment. 

"We give more tax relief to the arts than we do to small businesses," he said. 

FOX News' Jim Angle contributed to this report.