Couple of questions:
1) How much have you paid to date??
2) Do you have the materials purchased??
3) What percentage of the tile has been laid (if any)?
4) What reason (if any) does the 'handyman' give for the new price??
As to your specific question, you are only obligated to pay the originally agreed price. That is the verbal contractual agreement. Based on your version of the issue, you will not be liable for the 'new' price since it was not accepted by both parties and a contract cannot be modified or altered unilaterally (by one party only without the other's acceptance).
As for the issue of small claims court.... it depends on how much you have paid, and what you have received in return. For example, if the handyman has completed all the labor and you have paid for all the materials, plus $700 labor, then you have not been damaged and have no basis for a lawsuit. But, if you have paid the full $700 labor and the agreed work has not been performed, then you could certainly sue to recover the additional cost that it may take to complete the agreed labor. Finally, you could also sue for any paid materials that you do not receive.