The main issue is forbidding campaign commercials of certain kinds within 60 days of an election. This is an obvious restriction. More generally, any law that restricts what someone, rich or not, can say of a political nature is restricting free speech. This is particularly ironic in that political speech was the main thing the First Amendment was designed to protect.

Check this out. This is from 1997, but the Democrats have been pounding on this since they lost power in 1994 and determined to get it back and never let it go. Note Fritz Hollings, who has been pushing a Constitutional Amendment to this effect for some time. The most recent was S.J. Res. 4 from last year.