Brooks didn't mean to kill Sumner, but lets say that Sumner dies within a day or two.
Brooks would be the southern John Brown. That is, a martyr-like figure with admirable qualities (Brooks was actually a decent guy, by all accounts) who nonetheless is clearly guilty and whom the extremists support and others on his side secretly admire while the moderates are disturbed and rush to denounce.
*assuming* that he is convicted. Would he be tried by a DC jury? I don't know the legal system wrinkles, but if he gets off through jury nullification that will be a big furry deal.
Apparently OTL he was convicted of assault, so there's a decent chance that ATL he gets convicted and hanged. But hanging a guy you're fond of is different than convicting him of assault and levying a fine. So there's also a decent chance he walks.
If he does get hanged, I think the result isn't much different than OTL. But if walks, I think its going to make things much more bitter faster than OTL, and that could have all sorts of knock-on consequences. This happens during a presidential election year, mind. Would it be enough to get Fremont elected? (Ugh, what a disaster that would be). Not that Fremont will even necessarily be nominated in ATL. It will also happen right before the Democratic National Convention. Would Buchanan still be nominated? Or with emotions high, might you end up with a deadlocked convention where either southern/doughface democrats or Douglas democrats walk out? If the latter, you might see some kind of Douglas/Republican fusion ticket, which would be a hell of a thing. This might actually be the best chance for Douglas to get elected.
What if John Brown comes east to assassinate Brooks after Brooks is let off?
Wiki says that Brooks fellow South Carolinian congressman Keitt held off Senators who were trying to rescue Sumner at gunpoint. What if one of these Senators is more courageous than OTL and decides to call Keitt's bluff. But in the heat of the moment (Keitt and Brooks were obviously *very* worked up at this point), Keitt shoots the guy. Or he makes a threatening gesture, the Senator grabs the gun, and in the resulting struggle it goes off, killing the Senator? And within a day or two, Sumner also dies.
That, Ladies and Germs, will officially have kicked over the sh*tcan.