If Erdogan doesn't back down? Almost certain. The government has gone past the point of no return for this just dying out. The funny part is that this would probably already be over if they hadn't cracked down.
The funnier part is that if it does boil over the U.S. probably won't support the rebels because they'll have a real chance of reforming a secular democracy.
I don't know what makes you think that. From both an idealistic and pragmatic standpoint, the US benefits from siding with the protestors and loses from siding with Erdogan, who is both Islamist and trying to move Turkey out of the US-EU power bloc.
The new regime probably will be more anti-USA than Erdoğan. There is a lot of people hating Tayyip for all the ass-licking he did for USA. The majority of protestors also doesn't really like USA much, not to mention that everyone hates capitalism and imperialist countries. "Imperialist" is a label that got stuck on USA for years in Turkey. The youth of this nation is heavily socialist/communist/nationalist, all of these labels clash with the "Imperialist" label.
To be honest (and blunt), nobody gives a shit about EU registration process in Turkey anymore. We all talked about how awesome would it be if we were in EU for years but that news trend is over. Turks do see themselves as Europeans and they pretty much dislike Middle-Easterners because they seem uncultured and barbaric to them but I'm not sure if people want Turkey to be in EU anymore. It's very clear that Turkey is not wanted in EU, and the Turkey is simply looking for alternatives. "There is no friend of Turk, except for Turk" is a Turkish saying that got stuck since the World War I, and there are people who are prejudicial against western countries. There is also a group of people who say that Turkey should return to it's roots and improve relationships and establish partnerships with other Turkic countries.
It's generally agreed even by people who hate AKP, that EU will just slow down the process even if Turkey met the required criteria. So it's mostly considered impossible and not important enough to even try.
These are just my estimations, the only (and most recent, 22 January) poll I looked at had this:
%33,3 Turkey should keep trying for full membership
%25,2 Full membership should be given up and there is no need for improved relations
%19,7 Full membership should be given up but partnerships must be established
%14,6 Not only Turkey should give up on full membership, we should establish an anti-EU structure (I think this means joining an organization that rivals EU or something)
I'm not someone who trusts polls too much though.
Turkish sourceTaksim is calm, but incredibly crowded.
Police is attacking protestors in Ankara... after they said that they weren't going to intervene until Monday.