Blood testing?

Hey all.
I'm an immigrant to the USA (been here approximately 6 years now), and I'm still in the process of finishing receiving approval to get a "Green card"; basically a document allowing me to work in the country, as well as granting me semi-permanent residency.
One of the final stages is getting a federally approved physical checkup; basically they're going to check me for any diseases or nasty shit that they don't want immigrants bringing in to the country.
However, I've heard rumors from those who've gone through it that the blood they draw is also tested for drug use of any kind.
Obviously if there's any traces, they'll jump on any excuse to deport me.
I'm just wondering - I'm a semi-regular cannabis user (an average of maybe twice a week); how long (if at all) does THC stay in the bloodstream? And/or, how long before the blood test can I smoke without fear of any trace showing up?
I've been clean for a few weeks now, but I'd really love some confirmation from anyone who knows whether or not blood testing is a viable method of determining drug use, and/or to hear from anyone who's been in this situation themselves.
Thanks.