If the law is declared unconsitiutional then the supreme court in your state will throw it out. Frankly the constitution doesn't guarentee you the right to carry 8 rounds or more in your magazine. Such things were not yet contrived in the 1780s.
As far as I know, you cannot impeach a governor simply because you don't like the fact that he supported a bill that your legislature passed into law. Moreover, it seems to me that your states electorate(the majority of them anyway) is actually quite pleased with the outcome.
You can always move you know....