Does the college name count?

[Mike]

So I'm a sophomore in HS right now and starting to look at colleges. So far two vantage points have been thrown at me.

Go to a smaller school, get your bachelors degree and then go to a big name school (MIT, CMU, Caltech, etc.) to get your graduates degree.
From basic logic, I know this will save me money. Compare a $7,000 UCONN in-state tuition to a $40,000 MIT tuition. However, when I go for a job interview at Big Company after graduating from UCONN, will someone with a degree from MIT get a better shot at a job then me?

Go to a big name school for your bachelors. The bigger name will get you bigger jobs.
Well, this would cost me a lot more money, but if it's true I may also be able to pay that student loan off faster. Does the "Wow, that guy went to School X!?" factor count much in a hiring process?

So, from your experience, does going to a bigger name school get you more/better jobs than going to someplace smaller?