Worse--you cannot be a TA first year except in very special circumstances (where you would find a TAship for an undergraduate class whose subject you have a PhD in or something equivalent; and then you would be competing with PhD candidates). The TAships offered through the medical school are for 1st year classes. Understandably, you cannot TA for a class which you have not taken and for which you are currently enrolled.
Just to clarify a few points, basically any PhD student in the sciences, particular at Stanford has full funding for tuition and living expenses stipend. Most departments/programs (there is a difference, for example Cancer Biology is a PhD granting program, but not a department) also have a TA obligation as a graduation requirement. Both because they need to people to staff the intro physics labs, etc, but also because they want people destined for academia to have some practice in teaching and working with students. However, there are tons of other TA spots that float around, and when they send out an email along the lines of "looking for a TA for X" to the biosciences grad students and med students, most of the bioscience students aren't interested, because they already have full funding and are busy with their own things.
Also, although not common, it is sometimes possible to TA a course which you have not taken and it is also possible to TA a course (or at least get a TAship type funding) for a course which you are also enrolled in. For example, a newly created course (and there are always newly created elective courses that come and go) needs someone to TA that class. Some people have even created their own seminar or elective courses and gotten to be the TA of it.
This is an extreme example, and not super relevant to your concerns (particularly because it involves an MD/PhD student), but it is the only example I can think of that has news stories written about it:
http://www.scientificamerican.com/article.cfm?id=exposing-the-student-body
Keyan pushed for there to be a personalized medicine and genomics course at Stanford, and because one of the aspects was controversial (having the students in the course genotype themselves), it took a whole year to get approval, but when they created the course, he was in charge of it.
As noted, that's an extreme example, but it happens all the time on a smaller scale with other areas. For example, a second year med student initiated a course on "lifestyle medicine", got it approved with a faculty supervisor, arranged different speakers from Stanford and outside of Stanford, and of course got to be the TA of it and basically ran the course, which was just a series of interesting lecturers. This is not going to be something you would do your first quarter, but I mention it as yet another option. I'm sure similar things happen at other schools, but one benefit of the extensive resources at Stanford is that if you have a good idea you want to pursue, there is funding and support to make it happen.
As mentioned in a previous post, you can also get funding to help out in some way for a course you are taking. I once got a small TAship to run the video recording of a course I was taking (most rooms have automatic recording capabilities, it was just located away from the main medical lecture halls). For some seminars and things they need someone to order food and take attendance, and that is often a paid job.
Anyway, these are still all modest pieces of funding when looking at the overall cost of education, but if people are very motivated and need to make money while enrolled, including their first year, if they look around there are lots of options.
I also want to clarify that the MedScholars project is not necessarily "research" in the traditional sense; it's a general "scholarly" project. I am sure this has been posted many times before, probably by me, but people have also done creative projects, such as a photo essay in a developing country or making a documentary, and there is not only funding to cover some of your tuition/expenses, there is also ways to get travel funding to do projects outside of Stanford and outside of the US.