If you have to pump the gas pedal in the morning to keep your car running, you may have a bad engine coolant temperature sensor. The computer in every fuel-injected car must know two things before it can figure out the correct cold-start air/fuel mixture: the engine coolant temperature and the outside air temperature. Your symptoms are a dead ringer for a bad engine coolant temperature sensor (ECT). The computer is calculating an air/fuel mixture that is too lean. That’s why pumping the gas pedal keeps your engine running.
You can have a bad sensor even without a “check engine” light or trouble code. I could tell you how to test it, but they’re so cheap (about $15) and easy to replace, that it makes more sense to just replace it. Ask the auto parts store clerk to find the right sensor for you (you may have two—one for the computer and one for the temp gauge on your dash) and to show you where it installs on your engine.