I think this is a bigger problem than SMP admissions.
When you apply to med school, faculty letters are non-optional, and you need 2-4 from science faculty. If you expect to get all your science letters from your SMP, that's a tall order, and you'll undoubtedly be questioned about why you don't have any letters from undergrad. So I think you have a general letter problem. Also, if you weren't recruiting faculty for letters, were you working on other assets for med school apps, such as volunteering & shadowing? These aren't optional either.
The reason an SMP wants to see these letters is that they want to see your med school app. They don't want to let you in unless you're a good bet for med school. The only missing piece of your med school app, when you apply to an SMP, should be a competitive undergrad GPA. An SMP can't fix a low MCAT score, immaturity, weak ECs, or lack of faculty letters.
In your shoes, I'd do 3 things:
1. Go back and beg. Target the professors you had who are most likely to be softies. Put together a package for them: a picture, your med school app essay, your resume, a detailed description of your performance in their course, and a thoughtful letter that asks for their help. Ask if you can take them to lunch or coffee, to get reacquainted. Get that nose good & brown.
2. Take another science class, such as at night, and get an A and a letter.
3. Make sure that you get a letter from your employer or your volunteer coordinator. These are usually optional, and won't be taken in place of a faculty letter, but a good idea regardless.
You can apply to SMPs without a letter, but I seriously doubt that you'll get into a quality program. I expect that you will need to wait a year, to build up your credentials (work, volunteering, improve your MCAT?). Rushing to get letters, just to get into an SMP, is asking for bad letters.
Best of luck to you.