WASHINGTON—Some American citizens who were denied stimulus checks this spring are hoping for another chance in the next round of coronavirus talks, a long-shot bid as Democrats and Republicans spar over whether families that include an undocumented immigrant should qualify for aid.

Under the package Congress passed in March, households were granted up to $1,200 for each adult and $500 for each child under 17. The law requires recipients to have Social Security numbers to be eligible. If a married couple filed their taxes jointly…

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