I expect that many ordinary Thais do support the coup, mainly because they are sick of the disruption and constant conflict. Whether that support lasts, of course, will depend on when and how civilian rule is returned. One difference from other recent Thai coups is the nature of the monarchy. The King has little structural power in Thailand, but enjoys enormous respect and power of persuasion, and he has played a key role in resolving other coups and domestic conflicts. King Bhumibol has been in place since the 1940s, meaning that for most Thais he has been a lifetime presence. He's now very old and in questionable health; he may or may not have the ability to force a resolution and it is not clear that the authority he enjoys will be passed on to a successor.

I do not think either the US or China has any meaningful role to play in the resolution: the Thais are and have always been extremely independent. They will trade with anyone, they will make security deals as it suits them, but they are not about to shape their own politics to suit anyone else.

I don't see the US being able to play the "China Threat" card to gain influence in Thailand, because the Thais don't see China as a threat. We saw a sharp division in the recent ASEAN Summit, a division that's been there for a long time but which becomes ever more evident. Vietnam and the Philippines see China as an immediate threat, Malaysia and Indonesia are on board with that to a lesser extent. Singapore stays neutral, while Thailand, Cambodia, Laos, and Myanmar heve no interest in an adversarial relationship with China. The closing communique from the recently concluded summit doesn't even mention China, despite prodigious effort from Vietnam and the Philippines.

One thing I've noticed is that unlike Latin America, where communist revolutions metamorphosed into left-of-center mainstream political parties, communist revolutions in the Philippines and Thailand were either completely suppressed (Thailand) or marginalized (Philippines). While the left-of-center parties in Latin America have a spotty record (as do their opponents), they do provide voters with a meaningful choice. In the Philippines and Thailand you have what might be called pseudo-democracy, with regular electoral exercises offering a non-choice between or among elite factions with little or no ideological or policy distinction. That of course yields a great deal of cynicism and frustration and opens the door for charismatic pseudo-populist demagogues with no agenda beyond their own power and prosperity.

A coup is not going to solve the problem posed by indistinguishable elite factions competing for personal advantage in a patronage-dominated system. I think it's likely that the factions will make a pretend peace and agree on a transition just to get the generals back in the barracks, at which point the game will begin all over again. Civil war seems less likely to me than a paralyzing routine of rallies and strikes leading to another military intervention. but many things are possible.

Long term, I don't know what the solution is, and I'm not sure anyone else does either. Clearly evolution is needed, but political evolution has been largely aborted by the dominance of elites that fight each other, but join together to protect the status quo that supports their privileges.

This article comes from a somewhat left perspective and is a bit chaotic, but makes some useful points about Thai domestic politics:

http://www.prachatai.com/english/node/2694