I know this thread is kinda old but I will be completely straight and honest with you. You can NOT get into ANY U.S. Medical School (MD..not sure about DO) without a Permanent Resident or Citizenship status. The only two ways to get a PR/Citizenship is through work (sponsorship) or marriage. Marriage is out of the questions unless you've been dating someone who's a citizen and can pull it off as legitimate. The fact that you've even posted this thread and that it can be tracked back to you makes it even more risky and of course, illegal. If you're caught you're going to be deported and will forfeit a chance of ever becoming a citizen. As far as sponorship through work goes, good luck with that!! Not only is it incredibly hard to get sponsored because the company must first place an AD for the position and PROVE to the government that there is no one in the U.S. that fill the role they are seeking you for, and that's why they want to get you a PR status. My mom applied for her and my PR through work (and she could apply for me cause I was still under 18 and considered a dependent) back in 2004. The cutoff date is 2002 for the current files in the Homeland office. According to our very trusty and incredibly knowledgable immigration lawyer, it would be another 5-6+ years for us to get our PR's and because with the change of the gov't (if it happens) the immigration is not a issue, the backlog of files is going to stay.
Why do I know this? Because I am a senior at an undergrad institution and I found out during my application process to medical schools last year that unless I can provide proof of my PR, they will NOT accept me. The closest one school got was that they said they would accept a document stating that my PR card is in the mail as the proof but nothing less. I'm sorry to burst your bubble but after going through numerous advisors at my undergrad institution, I can tell you that most advisors (teachers, fin aid, graduate/undergraduate advisors) are literally clueless about the shades of gray when it comes to immigrant students. I had to go through multiple rounds of talk with my immigration lawyer and my school's financial aid advisor to clear up the misunderstanding that as a DEPENDANT student of an H-1B worker, I do NOT need an F-1 visa to go to a school in U.S. and that there really is such a thing as "in between change of statuses" that can last anywhere from a few months to a many years (5 years and still going in my case). And don't even get me started on how crappy DMV is when it gets to renewing your driver's license.
Anyway, back your post, even the very few schools that do accept international students-- you'd better have a 4.0 GPA and 40+ on MCAT to stand a chance. It's next to impossible to get in as international students. Think of it this way-- you're LITERALLY competing with the rest of the world for 1 or 2 (or 3..I'm being generous with 3) spots in the entire entering class. And you'd better have a solid answer when they ask "Why should we chose you over current residents of USA?".. heck even PR card holders get asked why should they be given a spot in the class when there are US citizens who could potentially use that same spots? You'd have to be a genius (literally) to be granted a spot at these schools.
I really have no clue what to tell you except to say that I am in the same predicament as you and it absolutely sucks balls. Your only option is to go to Caribbean medical schools or get your masters/Ph.d/or work until you can get that nice little PR card. Or marriage.. but then again if you get caught you are seriously jeopardizing your entire career.
EDIT: Fortunately for me, my boyfriend and I have been dating for over 4 years and we've casually mentioned marriage before so we *may* get married but then again, I am like you and I want to make 100% sure that he is the ONE for me. My current course of plan includes completing my masters/Ph.D and getting some research out of the way and then applying to medical schools. I have numerous friends who are in medical school now who took a couple of years off (most took 3-4 years off) and are now successful residents.