[Won]

Spit, stumble and intake backfire all sounds like a lean running condition. Improper mixture setting, unmetered air (vacuum leak), or out-of-adjustment WUR are a few things that might cause the condition. If it always runs well from dead cold then starts spitting after certain time, then the WUR is a likely suspect.

Try this:
take off the air filter cover and slightly lift up on the air meter arm that is connected to the metering plate (if not familiar with it, follow the path of air through filter and towards the rubber boot up top and you'll come across it) while having someone start the engine. That will temporarily richen the mixture; if the car was running lean, this will make it run better. If there is an improvement with richer mixture, then you need to figure out what's causing lean mixture and fix it. Be careful not to get caught by the fan while you're doing it, watch your fingers/necktie/shirts, etc.