Well, in theory it shouldn't matter whether or not the republicans have a majority in congress. Or if it DOES matter, everything that old Montesquieu-fellow wrote about trinity of power is scrapped in America and it would mean a bunch of other (nasty) things.
For those who don't remember anything about Montesquieu and his writings, he developed the theory of power being divided in three parts in a proper state: legislative power, judicial power and executive power. These three entities should be entirely separate from each other.
Basically in US the legislative power is on congress and senate (according to my understanding). Government has the executive power only, and the courts have judicial power. Legislative power is the highest of these - other two (should) wor along the rules set by congress/senate. In ideal conditions all of these parts of power work independently and one person or concil or whatever only has power on one of these branches of power, and
If, however, the legislative power manages to also have control over jurisdiction, then it results in situations like Silvio Berlusconi setting a law that makes the prime minister (conveniently) impossible to prosecute during term of office. Or, like it's suggested here - if the congress/senate manages to meddle in this matter so that Bush gets away with it (again). That's called corruption in some groups; in some groups it's called "national security".
