I'm not talking about open market operations via the Federal Reserve bank, or indirect payments through lower taxes, but rather the U.S Treasury simply cutting checks and mailing them directly to taxpayers at the behest of the President or legislation passed by Congress. To avoid raising the National debt, the U.S. Treasury would fund the payments by increasing the monetary supply (i.e., printing more money).
Note: My question isn't quite an exact duplicate of this question, which isn't directly asking if, under certain circumstances, the government can legally bypass the Federal Reserve and issue its own currency.