The sad thing is, yes they do. There are a still a lot of democrats who just cannot bring themselves to admit that Obama is a massive hypocrite and liar. Obama took the surveillance program Bush and Cheney set up and expanded on it because he wanted to. He is not liberal, he is not progressive. At best, he is slightly left of what currently constitutes republican, at least on social issues. When it comes to economics and corporate issues he's mostly in agreement with the conservative establishment. He wants to cut taxes on the wealthy, he wants to lessen regulations on the banks, and he wants to cut social programs to help pay for those tax cuts and the out-of-control spending of the Department of Defense.
Even his healthcare law, the thing he brags about every chance he gets, is based on a republican law originally thought up by the Heritage Foundation (a large republican think-tank). In fact, there are starting to be reports coming out now that while he was campaigning for the law, he was actively trying to sabotage the single-payer portion that was originally a part of it (before all the talks of 'death-panels' derailed that debate into idiocy and the single-payer option got cut). A healthcare law with an individual mandate, but without a public option, is just one big handout to the insurance companies, in the end.
Even with Obama giving lip-service to the idea of 'reforming' his surveillance program... I still wouldn't let myself get caught out in any wide-open, witlessness places if I were Edward Snowden. One thing Obama has shown himself to hate more than anything are leaks. Especially leaks that make him look bad. He's charged people with the Espionage Act literally more times than all the other presidents combined. The fact that the NDAA allows him to execute US citizens abroad without a trial is also especially worrying in Snowden's particular case.