some games are just utter trash...  do the developers realize this?  or do they convince themselves it is a masterpiece? 

obviously someone wouldnt want to think that their game is crap...but could they ignore how bad it is?

Do they know they are wrong? Yes.
Are they going to admit? No.

I think they try to do what they can under budget and within the schedule their publishers give them, and its sacrifices due to these things that can turn a game into trash

Yes, but many times they are being pushed to get the game out the door. Other times, its to fit the requirements of the license holder or publisher.

Yes, some do...

Didn't EA time back mention that their investors didn't care about the quality of their games and that they only really cared for the sales.

If it makes a profit then they don't care.

Some do realize, that their game is trash, but publish it anyway for the money/can't afford not to publish it/the devs just do what the publisher says to do.
And the others who don't, think themselves as artists, making the worlds greatest game, and then complain when Frogger sells better than their trash.

They realize it. But they want money.

I don't know. Sometimes when I did something myself (like a task) I have the feeling that it is good but at the end i hear it was bad can also be the same case for game developpers.