Given that the goal was to create an economic stimulus by getting more money in consumers' hands, it would have been much smarter simply to reduce the FICA withholding rate a little. Immediately, everybody's take home rises. No several month delay. No expense to print and mail checks.
Yah, but that is logic ... and logic is the antithesis of what politicians do for their own power. If what you suggested actually applied, then politicians wouldn't be able to state in their (re)election campaigns: "I did THIS for YOU"