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Mr. Smith’s bill would invalidate those laws, which prompted Democrats to accuse Republicans of overriding states’ rights.

“Until we step up and do the job, I don’t think we should be pre-empting anybody trying to deal with this issue,” Mr. Berman said.

Republicans, who have argued states such as Arizona should be allowed to enforce federal immigration laws, said in this case a uniform standard would be beneficial for businesses.

But in an overture to agriculture businesses, who rely heavily on illegal-immigrant labor, the bill Mr. Smith wrote would have allowed them to exempt returning seasonal workers from being checked.

Democrats and some Republicans said that amounted to an “amnesty” for illegal immigrants who already hold farm jobs and who could just keep returning year after year to those same jobs.

The two sides combined to strike that provision from the bill.