Well, your post is lacking some information. What were your groups with field points and at what distance are we talking about? How about some info on your setup such as bow weight, draw length, draw weight, what spine arrow and such.

There are several things that can cause groups to be larger with broadheads. One would be that the arrow spine is too light for the bow. Another is that the broadheads are not aligned (spin test) with the arrow shaft. It could be that the FOC of the arrow is too low letting the arrow drift so groups open up as the range increases. It could be a fletching contact issue. Most of these are related to:

It could just be a tuning issue. The bow/arrow combination might not be finely tuned enough. Field points won't show slight imperfections on shooting form or bow tuning near as much as broadheads.