Going from practicing democracy to a dictatorship...that a tough one to swallow.
Considering that their main head-quarters was obliterated along with what was essentially their entire government and the majority of their population, a change to a martial-law dictatorship is perfectly reasonable.
Actually its more than reasonable, in my opinion its completely necessary at this point. The Enclave by Fallout 3 is essentially a military organization anyway, there really isn't such as thing as "civilian" politics.
I don't know if you've read Tom Clancy's novel "Executive Orders" but the setting of the book closely mirrors the Enclave's situation (although for the Enclave its even worse). Essentially the main character is the sole surviving member of the government (he's the VP) after a terrorist attack takes out just about every member of Congress, the President and most of his cabinet, as well as the Supreme Court justices, which basically leaves him to lead the entire United States Government.
Again this is stuff that total speculation. Is it possible there is or isn't a Congress? Yes.
Possibly. Its also possible that Eden has a cabinet. We simply aren't given enough information. The only leaders of the Enclave we know of are Eden, Autumn, and the "Enclave High Command."
Pretty sure on Eden's radio message he blabs about Congress
He actually never mentions congress. He talks about the "Capitol Congressmen" baseball team. But the word "congress" in the context of the American Government is never discussed at all.
Proof: (read the speeches) http://fallout.wikia.com/wiki/Enclave_radio
Swearing your loyalty to someone is different than being a fanatic who will give up the basic instinct of preserving your own life.
Considering the Enclave soldiers often say "For....Eden...." on death. We can presume a near religious loyalty to the man (err..well..computer). They are essentially equating Eden with some sort of God-President. Its not
quite that extreme. But at a time when most people would be giving a last rites confession or thinking of family members or friends, their thoughts are for their leader. That's borderline religious devotion.
A whole Senate (you'll have to excuse me if those are both the same thing, I've never been sure; I think it's like the House of Commons and then the House Lords here in the UK).
"Congress" is the term for the entire U.S. National Legislature, (ie. Both the House of Representative and the Senate).
As far as I know, the Senate is roughly (although not exactly) equivalent to the House of Lords, while the House of Representatives more closely resembles the House of Commons.
Although I'm not that well-versed in UK politics myself.