Hiya,
Not really enough information to go on, so I'll put forward some of the initial thoughts..
I'm presuming you are both American citizens, here on a work permit and that's due to last 1-3 years or so.
You 'Can' get a mortgage - just depends on how much of a deposit you can put down really. Other factors come into play, what kind of jobs do you have? are they high demand, and significantly well paying? i.e £40+K ?(read that as higher rate tax payers)
if you can put down a sizeable (25% or more during the years prior to the credit crunch, and now possibly 30-35% with the credit crunch biting deep) deposit, show a well paying secure professional career/job position - there will be a few mortgage lenders who'll be willing to consider you. Basically the above is what 2 of my cousins did after being here for around 10 months or so as medical professionals around 2003ish. They had no credit history really but with the amount they were making combined, plus a 10% deposit at the time on a sensible (for them at the time) 1 bedroom apartment - the mortgage was approved with no hassle.
if you aren't in that kind of career/job and have a substantial deposit, you'll probably get approved, albeit with a higher interest rate - if you can show you are looking to live here long term it'll probably increase your chances of approval.
If you are like the majority of potential home buyers in the UK - ie basic rate tax payer, 10% or less deposit - you are likely to be rejected in the current climate.
So really boils down to the addage - how much money have you got?!! the more you have, the more opportunities like this are progessable.
I'd also suggest appraching as many mortgage brokers as you possibly can - these guys specialise in re-selling mortgages to those in circumstances which means most of the traditional lenders have for whatever reason rejected them - of course, it might mean higher interest rates etc (watch out for other less well discussed charges - such as arrangment fees etc) but sometimes can be a good option to persue
good luck!
Cheers, DtM! West London & Slough UK!