No one is taking away the right of the people to peacebly assemble. No one is disbanding the NRA, they just have to disclose the source of the money used to buy the ad.
That means that Greenpeace can't buy an ad calling Bush an enviro-rapist using money from that guy who runs RJ Reynolds. They would have to prove that the money came from PEOPLE, exercising their First Amendment right.
So people would have to sign donor cards for $5 donations to their party? They wouldn't, probably. And there would go not only a lot of money but also the voice of the small donor in issue advertising.