Military Tenant "opt out" of signed lease prior to move in.

[Christopher Morin]

Hi all, to start I'll start to say that I'm new here, and very new to real estate in general.  So go figure I have an issue with my first tenant, in my first rental property ever.  I'm in Okaloosa county Florida. Here are the details.

The tenant contacted me while deployed (return approx 30 jan 2015), stating that they already knew what the property looked like and would like to hand over a security deposit to secure it.  I responded and said that they would need to sign a lease prior to me receiving any deposit.  So I had them apply, they had a friend do a walk-through, and I told them that the only way I'd "hold" the property was if they signed a lease with an effective date of 1 Jan, and they would owe me January rent (despite their return date of approx 30). 

The tenant readily agreed, and we signed a lease about a week ago via e-mail correspondence with an effective date of 1 Jan.  She said she would have her mother postmark 1st months rent and security deposit, which I have not yet received.  We arranged to hand over the keys on her return.

 I included in additional clause "Tenant acknowledged that even though they will not physically inhabit the home until they return from deployment (after the lease effective date) they are still responsible for the terms and provisions in this agreement."

Today the tenant asked for a reduction on the January rent, and I said no.  They then came back and said they "decided to opt-out of signing the lease."  Whoa whoa whoa!  After already delaying December's rent, now I'd be missing on January rent even though they knew the terms they were agreeing to.   There is no provision for early termination of the lease

So my question is, do I have a leg to stand on trying to pursue this if she "backs out"?  I am active duty military myself, I'm not trying to screw her based on her situation, but she fully knew everything she was signing up for.  Is this just something I have to write off as a loss?  Even if I can levy a damages judgement for lost rent, how can I serve them at an address when they never even moved in?  Looking for any advice you guys have...