“If we pay the rent, we don’t have enough money to buy what we need, not even vegetables,” said Mr. Arenas.

A provision in the legislation that created the stimulus fund, which received little attention while it was under debate, prohibits payments to people who file taxes jointly with someone who uses an Individual Taxpayer Identification Number, a common substitute for a Social Security number used mostly by immigrants without legal status.

The result, immigrant advocates say, is that many American citizens who are married to undocumented immigrants will not receive financial support at a time when the country is facing a staggering unemployment crisis.

Those families also must forgo the bonus payments that otherwise would be distributed based on the number of children living in their home. As a result, larger households in financial distress may lose out on thousands of federal dollars because of a single undocumented family member.

An estimated 1.2 million American citizens are married to undocumented immigrants. Michael Zona, a spokesman for Senator Chuck Grassley, a Republican who as chairman of the Senate Finance Committee helped craft the bill, noted that American citizens who file separately from their undocumented spouses may still be eligible for the credit.