The rest of the Syrian air force was attack-oriented in spite of the fact that it had little chance of surviving Israel's air defenses. Again, the IISS and Jane's estimate it included some 105 obsolete MiG-21MF/bis Fishbed, 15 obsolete MiG-21U MongolA, 50 obsolescent MiG-23BN/UB Floggers, 50 limited-capability Su-22 Fitter D, and 20export versions of the Su-24 Fencer with limited computer and avionics capabilities. It is possible that the Syrian air force has rules of engagement that preclude the use of fighter aircraft for anything other than all-out war given the massive losses they suffered fighting the IAF in 1982.
This makes the Syrian forces vulnerable to U.S. military action to enforce some form of no fly/no move zone, but Syria still has a much larger and more capable mix of forces than Libya possessed. It would take a massive U.S. air and cruise missile attack to suppress it quickly and would be difficult for even two carrier groups to carry out and sustain. As a result, the United States would certainly desire land-bases from allies like Jordan and Turkey and the use of Qatari and/or Saudi bases.
Syria could also choose to ride out a U.S. threat and then constantly push the U.S. by appearing to prepare its forces, locking on radars, etc. These are tactics that would stress any U.S. forces enforcing a zone. Syria also knows all about them from U.S. operations in Iraq and the former Yugoslavia. In short, Syria does not have strong air defenses by U.S. standards but it is still very large. It would take a major U.S. air effort to accomplish quickly and the United States might well take some losses if Syria fought back and would have to have a sustained presence if Syria chose not to fight.
There is also the question of how broad a U.S. no-fly zone would really be. If the United States included civilian protection areas, it would have to be prepared to use airpower to stop pro-Assad ground forces as well.
If it was a true "no fly" zone, it would have to deal with Syrian helicopters as well, and they have been key threats. (IISS pre-civil war estimates were 33 Mi-25 Hind D attack helicopters, Mi-17 Hip H and 30 SA342L Gazelle multi-role armed helicopters, and 40 Mi-8 Hip transport helicopters, and some 60 percent are probably still operational).
Moreover, "no fly" would presumably mean no Syrian missiles and rockets and Syria still has a significant inventory of such systems. In short, even though the events of the past weekend may suggest air power's efficacy in responding to the civil war, it will be no easy task to expand this into a wider campaign.