W-2 Incorrect State

Hello All,

I've incorrect state on the W-2 form (box 15). I've notified the employer but I think it's too late. What would be the procedure now? I've not yet filed taxes with IRS. 

 

I heard we need W-2c. How long does it take for the employer to generate W-2c? Do I've to wait for it or will I file taxes with the NY state?

 

Any lead is appreciated. Thanks.