Jerry Jones seems to have long term plans for Bryant, judging by his comments today regarding the situation. Some teams and owners can look past things, while others cannot. Jones has put up with much worse regarding Bryant and has pretty much gotten him under control, so I don't see this is being too big of a deal. Besides, he is an obvious top 5 WR talent who helps the Cowboys win, and Jerry Jones has seen this before with Michael Irvin, Deion Sanders, etc.
In the case of Bryant, the first outburst was caught on audio screaming at Romo "we're the best in the NFL at that. You know we are. We're the best at that. Nobody's better." The comments caught in the first "meltdown" were nothing but positive. Sometimes the media tends to blow things out of proportion and doesn't put things in context.
I'd be much more interested in hearing the second meltdown where Witten and Bryant exchanged words. That one didn't seem to be as positive, as both players looked somewhat heated (especially Witten).
That would never do it. They gave up a 2nd round pick to select him in the supplemental draft last summer, and didn't have a 2nd rounder this past April just to get him. I wouldn't see any reason why they'd suddenly want to get rid of him for much less, especially considering that they're probably close to competing at a .500 or better level with an addition or two at QB.
They have 7 of the first 120 picks next spring, with 2 firsts, 1 second, 2 thirds, and 2 fourths; so I imagine that they'll definitely be making some moves to get one of the QBs who are coming out in the draft. I would expect them to keep their defense intact along with young skill position players like Gordon, Benjamin (who just went down with an ACL tear yesterday), and Cameron, so that they will have something of an offense when they select their QB + get Hoyer returning as a backup.
They don't need picks. They need a QB and a RB, and to package a pick or two in the future for 2015, which they will likely do now that Lombardi is at the helm.