The Latin American Public Opinion Project has some data on support for democracy in Venezuela. The upshot is that it is high, and in fact even higher than in the United States.
We have to be careful about how we interpret this. It does not necessarily say that Venezuelans believe the country is being governed democratically. I expect many, particularly in the opposition, would say they believe in democracy, but not the way Hugo Chávez has managed it. On the other hand, it is undeniable that many Venezuelans do believe the country is being governed democratically.
Either way, the overall level of support is important as Venezuela moves into unknown political territory. At the very least, leaders on both sides will feel more domestic pressure to find democratic solutions to political disputes. With luck the United States will recognize this and resist calls for intervention. Beyond generic calls for all sides, the U.S. should stay out.