As it sounds like you're planning to pay the extra $ to do same day change and get on the earlier flight, the suggestion I'm about to make won't be of much use to you this time, but may be for future reference.

My suggestion is to not worry about checking luggage, and just do carry-on only. It simplifies life in general (because you're carrying around less stuff, and most people carry around a great deal more stuff than they need), but in particular makes air travel simpler, as you can much more easily adjust to changing circumstances.

Some sample scenarios:

1. Some sort of hideous airport screw-up at originating airport (weather would be typical scenario here; unlikely in Sacramento but I once had to work around a nearly three hour ground hold in Atlanta that was due to a broken plane stuck between runways) that prompts Continental to bus you to San Francisco and put you on an alternate flight, except that only passengers without checked luggage are eligible since the timing's too tight to retrieve the luggage.

2. You make it to Houston, but the first flight ends up being cancelled for mechanical reasons and the second flight is now grotesquely overbooked (as passengerss from both are now competing for seats on the later flight). Continental is now looking for volunteers to travel the next day or take alternate routing. If you decide to stay in Houston overnight (and get paid for your trouble), you won't have to wait for your luggage to be retrieved. And alternate routing is much, much easier.

I'd say there is not a chance that this is enough time, having almost missed flights at Houston. However, I read on and Seamus's info on where you arrive is helpful since you won't be arriving at the "regional jet" terminal which is eons away from anywhere else.
I suggest you tell your FA and the gate agent about your close connection and see if there is any way you can sit near the front of the plane.
Another time we were late for an international connection and the people near us were nice enough to let us get off before them. We were met at the jetway by a cart and taken to the international gate.

tarantism - there is always chance that an arrival or departure gate can be changed, but if you use the flight status search on the CO site you can look over several days to see which gate a flight usually uses.

In terms of booking directly, in almost all cases it is preferable to book directly with the airline itself. A big reason is that it lessens the chances for error as information is transmitted. An exception might be if you are getting an absolutely amazing price, but most airlines nowadays offer a price match guarantee - though this usually does not apply to tickets purchased from consolidators.

Your luggage may actually make the 30 minute connection, but carry on only is always a good idea if you can do it. And if you make the flight nut your bags do not they will likely arrive on the next flight and be delivered to your hotel (so make sure you have the address and number of the hotel with you when you arrive, just in case.)
BTW, CO does have new same day flight change policy. Starting 24 hours ahead of your scheduled flight you can call and ask to be switched to a flight leaving within 12 hours. Cost is $50. So you could call CO at the day before your flight try to get on the red eye that night (departs 1215 AM) or wait until 6 PM and try to the 605 AM departure.

It's absolutely criminal that the airlines sell connected flights so close together. I learned about this the hard way last year when flying back from Rome on American, changing planes in Chicago w/ 1 1/2 hour between flights. The Rome to Chicago flight was delayed, and in Chicago we had to walk for miles, retrieve our luggage, go through customs, recheck the luggage, another long walk to a tram that took us to another terminal, then a frantic dash to the gate. Miraculously, we managed to make the flight because it had been seriously delayed. It just defies logic. And I booked that flight over the phone with American!

Thanks so much for all of your help!

Update:
My boyfriend called Continental on Monday. The guy understood our concern, so he said he would change our flight to the one leaving at 6 a.m. However their "computer system was down," so we would have to call back later. Unfortunately, my boyfriend didn't take the guy's name down. He called back yesterday, and he talked to another person who wasn't as understanding as the first guy. He said that our flight arrives and departs from the same terminal, so we will have PLENTY of time… (Does anyone know where it shows which terminal we arrive in/depart from?) Then he said if we wanted to get on the 6 a.m. flight, we would have to wait standby. *Sigh*

I don't know where it would show terminal on tickets you got from cheaptickets as I never used them.

I don't think it's on the ticket, but on the itinerary, usually. If you can't find it or it isn't there, you can see it if you go try to price that exact flight on Expedia, and when it shows you the flight details, it has terminal.

Keep phoning Continental until you get a cooperative agent. Always works for me. Some are just more helpful than others.

Note that on Continental's website, that flight that lands as 12:05 has a 60% on-time record...

Yes, it is very frustrating. You might call back till you get someone as good as the first person.:)
I would think eventually you would get on the early 6am flight out of Sacramento....and perhaps by calling AGAIN(and again) you can get that changed when they see that the connection is too tight.
(I can't imagine the first domestic flight will take you into the International TErminal...from where you leave(but perhaps it will)...but I do know that they are within walking distance,,,(inside)!

Leaving Sacramento earlier, and getting that flight locked in would be your best bet , and I'd keep calling Continental,,,even asking for the "supervisor".
Good luck and let us know what happens.

Arrives and departs from Terminal C

See my comments on the "Airline" thread.