As mentioned above, AMA does advocacy. They are not a union and thus lack the teeth (or drawbacks) of a union. And while many may not be happy with the AMA, they're the only large and powerful lobbying group we have. My state medical association has actually done a lot for us on the state level, but the AMA handles all the national stuff. Medicare reform? That's all going to be advocated by the AMA on our behalf and no one else.
If you want the AMA to be more effective, then become a member and tell them to speak for you. Us physicians all wishing the AMA was more effective/pushed certain points stronger is pointless if we're not members and not providing them support.
Conversely, if you ever need to find someone, the AMA are the folks to turn to. They have nothing over the CIA or FBI. After about 10 moves (I was a member while in medical school, then cancelled), they have steadfastly tracked me each time, and rather quickly, sending their "dues request," within a few weeks or so of each move it seems. Ultimately I gave in--not because it was easier to just surrender, but because Laurel Road offered an interest rate deduction if you were an AMA member and over the 10 years or so of the loan it would save me a substantial amount of money. So now I can at least complain about the AMA and have a right to complain since I pay them.