The proof, as they say, is in the pudding.
Iranians haven't revolted en masse against the current government, so, logically, it has enough support.
Does this mean everyone loves IRI and agrees on every single thing, and has pictures of Khameini in their wallet? No, of course not. You have 80 million people with 80 million views.
Even among the government, you won't find people thinking the same. Even among the Guardian Council or Majlis or Assembly of Experts, they don't agree on a lot of things.
Keep in mind that IRI is an evolving system, that's the best thing about it. We used to have a Prime Minister! We don't anymore. Laws are constantly changing. I remember a time when families hid their music tapes in their house and now you have concerts in Burj Milad. Should be there be more concerts? Some believe so and are pushing for it. Should there be less concerns? Some believe so and are pushing for it.
The changes that are happening in Iran are a constant struggle between various groups to bring in the changes they believe in. But most reforms are LOCAL reforms, which is why we have one of the most stable countries in the region, EVEN though we have so many enemies!
One final thing. I sincerely believe Iran is one of the most democratic countries in the world. First of all, we need to define what democracy means. Democracy is a system of government, it's not a system of values! I've seen the word "democracy" be used in a lot of silly ways. For example, they say, if a country doesn't have certain rights for its people, then it's not democratic. Why? What has that got to do with the meaning of the word?
So, here's one definition,
"A system of government by the whole population or all the eligible members of a state, typically through elected representatives"
It has nothing to do with equal rights or tolerance or loving each other or not setting anyone on fire. It's a political structure. We like to make every word emotionally laden which, of course, makes it hard for people to understand reality.
As an example, imagine a small village in the middle of nowhere. These village has 100 citizens. They decide to have a democratic system. They vote in 5 people to form a council to pass laws. The first law they pass is to execute anyone with red hair. The village has 99 people with black hair and most of them hate people with red heads. They have a stupid belief that anyone with red hair is the child of the devil. There are a few tolerant people among them, but as a whole, they all hate red heads. So, once the vote is passed, everyone is happy. To make it even more democratic, they take a vote on the law, and find that 90% of them vote "YES" on "LAW 3833 EXECUTE RED?"
That might be morally repulsive, but it's democratic.