Disclaimer I am a Ravens fan (who I think are going to be the favorites next year and should have beaten New England this year anyway).
I think it would depend a great deal on where the picks are. I mean if one of the picks gets you RG3 than that is something you would probably have to do, but if you are talking about middle of the first round (or later) type picks, than I don't think you do it. The Patriots are pretty young, but have a lot of holes that need plugging, multiple high picks for a 35 year old quarterback, even a HOFer like Brady, it tough to pass up. Cleveland, for example, has two firsts this year, including #4, if the Browns offered both 1sts this year, its second, and a future second (that could become a first), than I don't really see how New England can turn that down.