The Senate immigration bill’s authors acknowledged Tuesday that their legislation does not require illegal immigrants to pay all back taxes, saying it would be too difficult to make them ante up everything they might owe.

Sen. Charles E. Schumer, the New York Democrat who is chief sponsor of the bill, said illegal immigrants by definition are living in the shadows, and requiring them to reconstruct their pay history could be tough — and potentially keep many of them from legalization.

“We all realize that the system is broken. We all realize that people did wrong things. And the goal is to set this right by letting those in the shadows come out,” Mr. Schumer said Tuesday as the Judiciary Committee plowed through more amendments to the 867-page immigration bill. “The worry I have here is that by being as rigid … as this amendment is, that it will delay and prevent many, many people from coming out of the shadows.”

The issue of back taxes is an emotionally charged part of the current immigration debate.

Mr. Schumer and the other members of the bipartisan “Gang of Eight” who wrote the immigration bill have said the legislation requires illegal immigrants to pay “a fine and back taxes,” and that is true — up to a point.

The bill says that before illegal immigrants can apply for initial legal status, they must have “satisfied any applicable federal tax liability.” That is defined as “all federal income taxes assessed.”

The problem is that the IRS will only have assessed taxes on work it knows about. At least half of all illegal immigrants work off the books, meaning their wages never came to the tax agency’s attention, and the illegal immigrants didn’t pay taxes on it.

Sen. Mike Lee, Utah Republican who is not part of the Gang of Eight, said that’s not good enough. He offered an amendment Tuesday that would have required illegal immigrants to prove that they don’t have any tax liabilities.

“If an immigrant has worked illegally in the United States for 10 years and the IRS has no tax records for that immigrant, then this bill would, by my reading, not require the immigrant to pay any back taxes,” Mr. Lee said.

His amendment was defeated on a voice vote.

Mr. Schumer said he agreed with the intent of the amendment, but said “the difficulty is when you get below the 10,000-foot concept to the reality.”

He said part of being an illegal worker meant not keeping records, and he didn’t see a way to make illegal immigrants go about recreating those work records.

Mr. Schumer said requiring all back taxes to be paid could prevent as many as 5 million illegal immigrants from getting legal status.

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