Reid said the package improves on a version passed last week by the House which would send one-time government checks of up to $600 for individuals and $1,200 for couples plus $300 per child to millions of Americans.
The Senate bill would allow the rebates to go to retirees on Social Security and disabled veterans that were left out of the House bill that was backed by President Bush.
The Senate bill also will tighten language to ensure illegal immigrants do not receive rebates.
Senate Republicans Wednesday blocked a broader Democratic stimulus package that would have extended jobless benefits for the long-termed unemployed. That bill also would have provided more tax benefits to businesses and allowed companies to write off more current-year losses against previous tax years, which would have helped home builders hit hard by falling home prices and the subprime mortgage crisis.
House Speaker Nancy Pelosi told reporters her chamber would act quickly, possibly as early as Thursday, once the Senate approves its version of a stimulus bill and send the compromise
to President Bush for his expected signature.
While she said she supports help for the long-term unemployed, she said that could be achieved with other legislation. "There's no reason for any delay" of the economic stimulus bill, Pelosi told reporters.
"The sooner we get this done, the sooner the checks will be in the mail," she said, adding the House would act on a Senate-passed bill by next week.