98 V6 Blazer Cold starting problem

Ok, here is my little problem. If the out side temp gets colder then 10 degrees it tries to start the first time I try, but only for a second, then after that it will just crank over until the battery goes dead. If I push the gas pedal to the floor while cranking it will try to start but wont stay running. Once the out side temp gets warm enough it or I just keep trying with a jump or the battery charger on start it will start at some point. Now, the battery is a new one with 850 cold cranking amps, also the alt and belt are less then a year old. I thought since I can try and start it for over 20min in below zero temps its not the battery so, I tried to put a little gas in the top of the carb and then tried to start it but nothing. I had it looked at by my mechanic and he did a complete tune up $450.00 plugs wires filters etc.. The next time it got cold out it would not start. He checked the fuel pressure and said its ok.
Once it starts it runs fine all day, if I leave it in the garage (heated to about 45 to 50 degrees) it starts in the morning no problem.

So in summary, its the cold (10 degrees or colder), does not seem to be the gas pump, has a new gas filter and is not the battery...

Does anyone have any ideas?

Thanks in advance..

Why do you say it's not the battery? Have you had it checked with a load type tester? If it starts with a jump start, then starts ok the rest of the day, and also starts when it's warm out, it sounds like a weak battery to me.

If the battery checks out ok with a load type tester, then I would look toward the coil, as cold weather will affect a weak coil.