US forces aren't strengthening the Green Zone Government, if anything they're the number one factor keeping it from establishing any legitimacy in the eyes of the people of Iraq. If Maliki tells America to fuck off, and we have to listen, then it would most likely cause his popularity to skyrocket.
The presence of US forces, however, reinforces the anti-GZG forces who claim (without stretching the truth in the least) that the GZG is nothing but a puppet regime controlled by America.
If we want Iraqis to take responsibility for their own country, that means they have to take responsibility for their own country.