What will almost certainly be ruled unconstitutional will be CFR's limits on ads (what can be said, when they can run, etc.). This is a direct first amendment question. FWIW, I have never believed CFR proponents took these limits seriously themselves; they are merely camoflauge. What the courts WILL let stand, however, will be CFR's limits on soft money contributions to the parties.
The practical effect will be that the Democrats will just let organized labor run the bulk of their ad campaigns with compulsory dues money. This is exactly what they did in '95-'96. All those grainy, out-of-focus ads attacking the "Dole-Gingrich Congress" were union ads, though most people don't realize it. (Thought they were Democrat ads, didn't you? Silly you.) All CFR will mean for the Dems, therefore, is that instead of writing large checks to the DNC, the unions will cut ads themselves. The same people make the decisions in either case, as the DNC/union political operations are, for all practical purposes, fully integrated.
The bottom line is, for the Dems it will be business as usual. The pubbies will have to scramble to find a new way to finance national ad campaigns.
An important thing to look for is a strong non-severability provision. I don't know if the CFR bills are written that way or not.
I should have added that the Democrats are counting on the courts to throw out the restrictions on ad content and timing. This will free the unions to do the "independent" expenditure thing, while the pubbies will still be hamstrung by the limits on contributions to the Party.