In America, I'm not sure we have such a good phrase for that. We might say "The elections were moved up by three months," but "moved up" is a little ambiguous as to whether it means earlier or later. Maybe "advanced by three months," but still that's not all that clear. I think the Brits have the advantage on us Americans here. In America, we do use brought forward in this sense: "He brought forward (or put forward) three ideas to help solve the problem."

In American English, having an event earlier than planned is to "move up", while having it later than planned is to "move back" or "push back". Think of yourself standing on a timeline, and the event date is ahead of you, in the future. So, if you move the event earlier in time, you "move it up (toward you)". And if you move the event later in time, you "move/push it back (away from you)". More discussion here: http://boards.straightdope.com/sdmb/showthread.php?t=467426

I wouldn't think it weird at all if someone said that in the US. I actually can't think of another way to say that other than something longer like "The elections are happening three months ahead of schedule" or "The elections have been moved to three months earlier than originally planned"