what is the impact of the tax rebate check on fiscal and monetary policy?

Answer 1

The rebate check represents fiscal policy. It is part of that policy, and is expected to help increase consumption by increasing disposable income.

Answer 2

This link discusses the house bill's stimulus package, which was close to the final stimulus package actually passed and signed.

www.heritage.org/Research/Economy/wm1778.cfm

Here is another from Brookings:
http://www.brookings.edu/opinions/2008/0205_stimulus_package_sawhill.aspx

One more from Marty Feldstein:
http://economistsview.typepad.com/economistsview/2008/01/martin-feldstei.html