Getting an apartment rented in less than 30 days

My apartment lease ends in July, however I was able to give 60 days notice to end the lease and move to a new apartment. I'm vacating at the end of February, but my management company advised that if no one rents the apartment then I still have to pay rent since my lease does not end until July. They originally said they would list it today on Streeteasy, but now said they don't want to do it until February 1st. This seems to be cutting it close and I'm nervous it won't get rented and I'll have to pay rent on two places. It is a no fee apartment in the West Village so I assume it will get rented, but it is winter so I know the market is slower. Do you think I will I be able to get it rented in under 30 days?