What effect would an economic stimulus loan, (repaid from loan recipients' income taxes) have on the economy?

If the two transactions occurred simultaneously there would be little if any effect. It is only because the government can borrow more and at lower interest rates than taxpayers and the loan will not be repaid when the economy is still bad, would you expect it to have a positive effect, and some economist do not believe the it would even then. If I know that in a few months I will get a bill for the loan amount I will just put the money in the banks so I can pay the loan back and I may do so even if I do not expect to get the bill for several years.