It's not simply the difference between "big" and "little" government, it's what each side wants to be big and little. The left in America generally favors a government that is more economically involved in people's lives, but takes a minimal role in controlling social issues. The right is seen as the opposite, advocating a government that does not interfere economically, but upholds a specific set of moral values. But it's important to remember that it's more of a 360-degree compass than a linear scale; many people's beliefs include aspects of both main categories. And of course, these lines blur when the government is in bed with big business, as is the case in our country as well as many others, I suspect.
Concerning the main issue, I think it's a good bet that if Bush tries to push the envelope, (even Rehnquist objects to many of the people on the list), Congress will make sure there's a gridlock.