Backers of the measure, already battling charges from conservatives who say the proposal amounts to an amnesty, acknowledge the problem and promise to fix it before the bill becomes law.

The problem is that the legislation, which would provide legal status to millions of people who entered the country illegally before Jan. 1, 2007, would establish loose standards for proving length of stay. Unless the standards are toughened, critics contend, there may be a rush to the border and a new flood of fraudulent documents.

“All across Mexico and other countries, the word will be vámonos – let's go,” said George Grayson, an immigration expert at the College of William & Mary.

Sen. John Cornyn, a Texas Republican, has been broadly critical of the legislation, which was forged in a hard-fought compromise between Democrats led by Sen. Edward Kennedy of Massachusetts and Republicans led by Sen. Jon Kyl of Arizona and joined by the White House.

“It sounds like an open invitation to fraud,” Cornyn said.

The budding controversy reflects the inherent difficulty in establishing standards of proof for millions of people who have been living with false identities in an all-cash economy.

The issue has been largely ignored as public attention has focused primarily on what critics call an amnesty and advocates say is the only practical way of solving the problems associated with a huge and steadily expanding population of illegal immigrants drawn primarily by low-wage jobs in service industries.

The immigration overhaul is intended to bring the estimated 12 million illegal immigrants out of the shadows. Kyl acknowledged he is concerned that number could grow because of fraud.

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