A loophole that would allow some illegal immigrants to collect tax rebate checks under the bipartisan House economic stimulus package will be closed by the Senate, FOX News has learned.

The problematic language is housed in the $146 billion stimulus package that passed the House Tuesday on a 385-35 vote. The plan would write checks between $300 and $1,200 to eligible taxpayers, hitting about 116 million U.S. households in a plan to boost the sagging economy.

But the plan isn't a foregone conclusion yet because the top Republican and Democratic senators on the Senate Finance Committee — Chairman Max Baucus, D-Mont., and Sen. Charles Grassley, R-Iowa — are backing a different, $196 billion version of the bill, and they'll get the first crack at the package Wednesday when the committee takes it up.

A senior Republican Senate leadership aide said the House package never intended to allow illegal immigrants to be eligible for help from the stimulus package, but some illegal immigrants could apply for the rebate under falsely obtained Social Security numbers.

Under the plan passed by the House, illegal immigrants who qualify as "resident aliens" and earned a minimum of $3,000 would be eligible for rebates of between $300-$600.

Only those illegals who have been assigned an Individual Tax Identification Number — which allows them to file income taxes — would be eligible. Resident aliens are defined as people who spend a "substantial" amount of time in the U.S. and have not been deported.

The details of the fix to the immigration language have yet to be worked out.

Asked about the loophole, White House press secretary Dana Perino said: "We know the issue has been raised and we are exploring ways to address it."

Also, Sen. John Ensign, R-Nev., intends to introduce an amendment Wednesday when the Finance Committee. Ensign's proposal would prohibit illegals from receiving the $500 rebate check that Americans would receive under the Senate version of the bill.

The Baucus-Grassley plan would set the rebate to $500 for individuals and $1,000 for couples. It also would deliver checks even to the richest taxpayers, who are disqualified under the House-passed measure.

Grassley on Wednesday told reporters he and committee Baucus hope to cast aside most amendments. It is likely Ensign will not be given a chance to offer his amendment. Baucus and Grassley want to get their bill to the floor as quickly as possible.

"If Baucus and I can work together, we can keep amendments down, keep it from becoming a Christmas tree," Grassley said.

The Senate could consider the House-passed economic stimulus package as early as Thursday, according to a senior Senate GOP leadership aide. The Baucus-Grassley bill will be introduced as an amendment: a full substitute to the House-passed bill. It is unclear if the votes are there to adopt the plan, however.

White House deputy press secretary Tony Fratto, traveling on Air Force One to California with President Bush Wednesday, said the disappointing fourth-quarter growth rate — which showed the economy growing at a dismal 0.6 percent — should give the Senate greater urgency to pass the bill House bill, which was negotiated between House leaders and the White House.

"We'd like to see some leadership that will encourage members to put away some of their pet ideas and think about the bigger picture," Fratto said.

He added that he does not personally support $14 billion in additional unemployment insurance for workers whose benefits have run out, but that he is willing to go along in exchange for Democratic concessions such as eliminating a provision that would phase out rebates for individuals and couples making more than $75,000-$150,000.

Grassley also praised the measure for giving rebate checks to 20 million senior citizens living on Social Security. The House measure would leave out many seniors unless they earn a paycheck or pay income taxes on their non-Social Security income.

Baucus' measure also extends unemployment payments for 13 weeks for those whose benefits have run out, with 26 more weeks available in states with a 6.5 percent jobless rate or higher. His initial proposal would have provided the longer extension for any state whose unemployment rate exceeded 6 percent, but the trigger was raised to control the cost of the package. Only Alaska, Michigan, Mississippi and South Carolina have jobless rates of 6.5 percent or more.

The Senate plan would restore a business tax break dropped during the House negotiations that would permit corporations suffering losses now to reclaim taxes previously paid.

Both packages include roughly $50 billion worth of tax incentives for businesses to invest in new plants and equipment.

FOX News' Trish Turner and The Associated Press contributed to this report.