Risks/problems of a short chain
To quote Sheldon Brown: "If the chain is too short, it will be at risk for jamming and possibly ruining the rear derailer if you accidentally shift into the large-large combination. Never run with a chain that is too short, except in an emergency." (I will say that depending on if your chain is short enough, it can happen in combos other than large-large.) 

Here is a good article on sizing chains. 

If its a new chain, I wouldn't hesitate in breaking the chain at a different link and adding some of the extra links back to it. But you really should get the chain to be of the right length before riding. 

Also, for what its worth, the easiest way to size a new chain for a bike which hasn't had a cassette/chainring size change occur is to start with the old (properly sized) chain, and use that to size out the new chain. Much less annoying than sizing the chain from scratch.