I Need to apply for OPT extension by May but employer is not e-verified and does not want to do it. Offered to apply for H1B but I will not know whether or not H1B is granted by May 2014 ? and by that time it will be too late to apply for OPT. Is looking for another job my only option?
If your employer applies for H1B Before the OPT expires, which is May 2014, you will be eligible for cap-gap based employment. You can read all the details at USCIS H1B OPT Cap Gap regulations