Based on the idea that Bran sees this, reports this and more reliable witnesses find them in bed or whatever I feel that Robert killing Jaime is the most likely outcome, if not just pitching his naked ass out the window on principle, then summarily executing him and no one daring to stop him. Cersei might actually be spared but only by the intervention of others, likely Ned Stark and Barristan Selmy etc if only to prevent fallout or whatever.
Combined with the fact that Catelyn's sister Lysa sent a letter to Catelyn stating that the Lannisters killed her husband Jon Arryn the night before and were plotting to do the same thing to King Robert, I think would lead to a very interesting political dynamic as the Eyrie, the Stormlands, the North, the Riverlands and likely the Stormlands as well as the Crownlands would all be pretty supportive of the King versus the Lannisters. And Dorne... would really have no issue with the Lannisters getting humbled.
Joffrey is actually convinced he's Robert's son (AFAIK) but it would seem rather apparent that might not be the case so him getting de-legitimatized might happen but it'd be just as amusing if not. The Lannisters really wouldn't have many options, practically speaking IMHO at this juncture. Robert might be furious and erratic because of this, and the cuckholding accusation would weaken his reign, but a Lannister gangbang would probably help centralize authority and Ned as Hand of the King would really help stabilize the situation.
With Jaime and Cersei either dead or captured (and Tyrion also captured most likely), poor Tywin would likely have to submit in a humiliating manner or go down fighting. Tywin ironically had no real part to play in this conspiracy, it was all Petyr Baelish and Lysa who did the poisoning so it'd be just as interesting to see if Tywin if he survives in some capacity, can be canny enough to figure out some part of the conspiracy. Also ironically, he'd probably need the help of folks who were his enemies in the main show.
Lysa is probably the weakest link and if Petyr can't control her, the whole conspiracy could end very poorly very quickly for Petyr Baelish if during the course of uncovering the mystery, people focus on Lysa and her seeming knowledge of the conspiracy ahead of time. That would be an angle that Tywin/Tyrion and the Master of Whispers Varys might pursue for different ends. For Petyr, provoking hostilities between the Lannisters and the rest of the Kingdom would likely buy him time to cover his ass as well as remove the Lannisters as a threat to him since he started the rumor implicating them after all.
The scenario would be more interesting with
@Bear Ribs idea of a major "good" character being offed but while GRRM might allow for that, I still don't see it. But I could definitely see Jaime Lannister and Cersei Lannister maybe escaping. But they'd still have to escape the entire North which... authorial intent might save them but practically speaking... would be chancy. Especially with those Dire Wolves getting a whiff of them.
If they manage to escape back to Lannisterland though I still don't see the political landscape changing much. The same people who backed the King before I think would back the King regardless of whether King Robert has Jaime and Cersei as hostages or killed or not. Their main value in being hostages is as bargaining chips for Tywin to submit and cooperate.