The tough part of it I see is that CBS for the last two decades has been a minor player in the sports rights game....
They're like a GM who will either sign an uber superstar (SEC marquee package, NCAA Tourney), or go with waiver wire pickups (Bullriding, XFL, AAF, etc). They're very set on what is acceptable terms and won't overspend in a bidding war for middling value
(I wish my baseball team's GMs were more like this).
So the question is, do they see NHL as a bargain value they can get on the cheap, or a property that's lacks universal appeal so they're not interested? I think a lot of NHL fans would be critical of Bettman if we replaced the SEC on CBS on a very small dollar contract just to up the exposure.
Of course, as a secondary contract, that could be a good thing, but at the same time, I think (a) NBC deal has exclusivity, so the NHL couldn't do a deal like that and (b), you'd be going up against college football. The NHL historically has done a terrible job of showing football fans why hockey is just as good/better... Going head to head with college football is a bad idea.