How to save medicare

I am taking a governmental accounting class this semester. Our first project was to come up with a solution for Social Security and Medicare. My first instinct was to make them go extinct. However that was a bit to simple for the required six page paper. After some research I discovered that the biggest problem was we are going to have less and less payers per beneficiary of the system. This leaves two possible solutions. Cut down beneficiaries or increase payers. The first option wont happen because the old farts that vote would never vote to increase the age at which they get benefits. That leaves the second option. The obvious answer to that is to increase the birthrate. The problem with that is that it will take 20 to 30 years for that solution to help. But alas I have the answer. Increase immigration. This way we can import payers to help fund the system. Best of all we don't even have to wait the 30 years for them to be productive.
Now I know someone out there is thinking but what about all the illegals drawing on the health care system etc. Let me explain what really happens. Immigrants with out Uncle Sams permission get a fake social security card and ID when they apply for jobs. Then the employer with holds the same 15.3% that you and I pay. Then occasionally when they are really sick yes they do go to the emergency room for care. Still I've got to believe even then they are net payers into the system.