No, there aren't any cheat codes in the Xbox 360 version of Mass Effect 3.
If you're having trouble with money or combat, you've got several options. At any point you can turn the difficulty down in the options menu if you think the combat is a bit too challenging. Further, the more you explore the galaxy, probe planets and scan systems, the more credits and other items you'll acquire.
If you do this early on in the campaign, you should have plenty of resources and find yourself having an easy time as you continue.
Further, if you download and install the free Kingdoms of Amalur demo, you can unlock a couple of bonuses in Mass Effect 3 - one is the Chakram Launcher, which is kind of a super-powered charge attack assault rifle, and the other is a unique armor set you get from the beginning of the game. Both of these could be considered somewhat of a cheat. :)