Just remember that the road of the past few decades is littered with broken hashes: MD4, MD5, SHA0, SHA1 and many others.
And yet bitcoin could use anyone of them today instead of SHA2 and there wouldn't be a security issue.
The fact that a weakness is discovered in a particular hashing algorithm doesn't necessarily mean that the algorithm is then immediately useless for all purposes.
If SHA2 were broken the breaker could mint coins at a faster rate than brute force. How much faster depends, could be tens or hundreds of times faster.. If the breaker is intelligent, he/she could slowly cash in over a period of a few years, walk away with a pile of cash and a world full of inflated Bitcoins. This would be an opportunity to cash in on research without the guilt of doing anything illegal or immoral. Don't look for them to publish a paper in ASIACRYPT14.
Another point, when a break is found it is usually followed by a improved break in a few months or so.