Big deal potentially equals 5.56 assault rifle pointed at your head by very unfriendly Border Patrol types.
Big deal potentially means getting getting up close and personal with Homeland Security types who take their duties very seriously.
Big deal potentially means you spending some quality with a cellmate of their choosing if you didn't leave your ammo and firearm on the other side because you illegal imported both. They are VERY touchy about that.
Big deal potentially means losing your firearm, being deported and having a ##### of a time getting back into the States again including something as simple as transferring planes in the U.S.
Big deal potentially means losing your firearms and hunting licences on this side when you get back.
You might, just might be able to claim ignorance that you didn't know where the border was and thought you were still in Canada. But if you knew or they think you knew they will make a big deal about it.
You can decide whether a game animal is worth it. If I knew it had crossed I would keeping hunting on my side of the line.