CQ Politics offers this report. See also these thoughts from Adam Bonin, Ed Morrisey and Instapundit, who calls this an incumbent protection bill. I’m not sure I see the incumbent protection here, but I do see an emerging divide (as I predicted) between Democratic and Republican support for the measure.
The CQ article quotes me as saying that courts have upheld false campaign speech laws in the past (that’s true, see chapter 11 of the Lowenstein and Hasen casebook), including those that had some kind of cease and desist/injunction aspect. I may have been wrong on that. It has been a while since I looked at the issue, and I note that the Pestrak case described in chapter 11 rejected “cease and desist” orders as violating the First Amendment. Before I delve into this more deeply, I’d be interested in hearing from anyone who can point me to such a system that has been upheld by a court.