To the OP, it sounds like your concerns stem from the fact that your school is very much in favor of a healthcare reform bill, but maybe you haven't been presented with enough information to feel like you can have an informed opinion on the matter.
I'd really encourage you to read up on it yourself, as at least in California, this legislative season is very likely to see some major changes in health care, and if you have a strong opinion about how things should go, you should get involved. You can find out more info about SB-840, which is Senator Sheila Kuehl's single-payer bill here
http://www.csphr.org/sb840, including a summary and information about financing the changes. AMSA is strongly in favor of this bill. Currently, the governor and Representative Nunez also have proposals as well, although they are not as comprehensive.
I am personally a strong supporter of single payer health care, and this is why:
1. I do believe that health care is a basic human right and everyone should have access, regardless of their immigration status or ability to pay. I realize that not everyone agrees with me on this one, particularly when it comes to undocumented persons. I think it's just good public health policy to ensure that the entire population is covered. And if you think you're not currently paying substantial amounts for other peoples' healthcare, take note of the fact that 60% of all US health care dollars are spent by the US government, a.k.a. taxpayers. It is also the case that in the current system, many people who would want insurance simply cannot get it--because they can't afford it or because they have a pre-existing conditions. It seems unjust to me that the person most in need of health care (say, a diabetic or someone with a history of cancer) is the person who is denied coverage.
2. Single-Payer saves time & money. Currently about 30% of all healthcare spending is due to administrative costs created by for-profit HMOs. Compare this to the 4% administrative cost of Medicare--a single payer system. By having one organization handle all the administration of the health care system, that money could be spent on patient care, not to mention physician reimbursement.
3. Single-Payer promotes economic growth. People would not be tied to their jobs because of their health benefits or worry about being denied coverage due to pre-existing conditions when purchasing individual insurance. This encourages entrepreneurship and helps businesses remain competitive with companies in countries like Canada and the U.K. that don't have to pay for their employees' health insurance. When Starbucks spends more on health care than coffee, and General Motors spends more on health care than steel for cars, it's easy to see how it's bad for multinational companies trying to compete in the international arena.
4. America is doing something wrong. We spend double the amount of money per capita on health care than the average of all
industrialized countries, yet we rank #37 in terms of health outcome (WHO data), and even worse when it comes to access. We are also one of the few industrialized nations that doesn't have a single-payer system. A publicly financed single payer system diminishes cost-shifting, provides greater bargaining power for drugs and medical devices, and eliminates tons and tons of physician time and expense in billing and paperwork.
5. Expanding coverage saves everyone money and improves outcome because people will have access to primary and preventative care. Everyone knows that the most expensive--not to mention inefficient place to get primary care is the ER, but this is where the overwhelming majority of uninsured individuals seek care, and usually after a delay. Since ERs can't refuse most of these patients, the tab often ends up getting picked up by the government (taxpayers).