That, my colleague is known as 'scope creep' and is one of the oldest problems known to freelancers.
It sounds in like they may be abusing the fact that you are 'not living around the corner'. I avoid working for companies that I cannot drive over to and meet face to face. There are too many people willing to twist things or railroad others in order to increase the scope of the project in their own favour. Distance working can make things even harder in that case.
A lot depends on whether or not the client provided a project brief based on 'time period' / price per hour or 'piece work'. Piece work can be a problem with clients you are not familiar with. I would in the future demand a 'per hour' or 1/2 day or Full Day rate. And make sure to clearly define what a Full day means. Mine is 10 hours inc travel time but not inc travel expenses for example. I also have a different hourly rates for different services.
You need to re-read all communications from them and see how vague / exact the wording is. Words such as 'may' vs 'will' vs 'plan to' can mean different intentions. I shared a house with a solicitor for 2 years so I know a bit about how subtleties in wording can be misused.
The best kind of work is via referral and then at least if 'Dave' treats you badly you can at least complain to one of his peers or do some form of moving and shaking. I find that works quite nicely. Of course you never keep all of your clients in just one group though. That can be equally dangerous for obvious enough reasons.
As IANAL indicates - surely freelance.com has some form of protection for this kind of thing anyway.
In addition I would certainly advise that you take out professional indemnity insurance so that in the future you can counter their threats with a lot more confidence. An email threatening to sue you can be countered with 'do it!' and no sleepless nights. It costs around £20 to £30 per month in the UK presently (Oct 2013).
I doubt that they are going to sue. They're just trying to push you around.
Finally, if it is not easy to physically speak to your client because they are 'too busy' or in a different time zone etc then I'd wonder why they were tendering the work out near you in the first place....