When you discuss the matter of government with libertarians, they will rail against the inefficiency and ineffectiveness of government. They will talk about the superiority of private enterprise, because they say that the incentive of profit drives better efficiency and performance. If you just try to argue back, trying to defend specific government institutions, you will probably not win. The Libertarian will have an endless string of examples where various government institutions have failed in one way or another.
In order to successfully argue in support of government, you need to reframe the discussion. You need to step back and ask the question, "What is government?" You have to define government in the right way in order to have a chance of defending it. I like to define it this way:
Government is a body of people banding together to solve problems that cannot be solved by the profit motive.
When government is defined this way, it becomes clear that government is to some extent necessary, since not all problems can be solved by the profit motive. Some of these require an appeal to one's desire for the betterment of humanity; examples are education, health care, and poverty. You may be able to convince some people based on this track. However, others may be a little more self-interested or independence-minded, and would argue that each person needs to lift themselves up by their own bootstraps. But, even for the people who "have it all," there are still some problems that cannot be solved by the profit motive. Some good examples are pollution, consumer protection, and infrastructure.
Pollution: If you are a factory producing goods, there is no incentive to do it cleanly; using processes to reduce pollution costs more money. The profit motive in fact works against the environment. The only way to solve the problem of pollution is to use government agencies to regulate it. If you live in a city and you can see blue skies, then you can thank the government. If you have clean water come out of your tap, you can thank the government. If there are still animals in your regional parks, you can thank the government.
Consumer protection: Private corporations have every incentive to provide worse products for more money. Have you seen the quality of the crap available in Wal-Mart these days? Have you ever heard anyone say, "they don't make 'em like they used to"? Also take a look at insurance. Insurance companies have all reasons to deny more and more claims and raise premiums. See health care insurance in the United States. The only thing that makes companies fearful of hurting consumers is the possibility of being sued. If there was no government, nobody could sue corporations, since there would be no judicial system. There is also the matter of medical safety; without the FDA, nobody would know which medicines were safe and which weren't, and large numbers of people would likely get sick and die due to medicines not being tested properly. You can thank the government for all sorts of safety precautions that give you safe cars, safe electrical systems, and safe food.
Infrastructure: There is no incentive for the private industry to build roads, bridges, and transportation for any areas but the most populated ones. If the government didn't build infrastructure, no rural communities would be accessible since there is not enough of a profit in building roads to them. Bridges are prohibitively expensive to build; it requires a large pool of money to undertake their construction. Both our rail infrastructure and airline infrastructure required significant government resources to create. Our economy would be significantly behind the rest of the world if we had not built this infrastructure, and everybody is better off for it.
Overall, there are some areas where the profit motive is a beneficial incentive, and there are other areas where it is a bad incentive. For areas where optimizing profits produces detrimental effects, we have to use the government as the solution instead of private enterprise. We cannot sacrifice everything to the altar of profit and efficiency. Even though non-profit motives result in lower efficiency, we must accept this reduced efficiency as necessary in order provide a net benefit to society.
Armed with these talking points, I hope you can have more success in defending the government against your Libertarian friends. The government needs all the help it can get, with all the anti-government attacks the Republicans have been throwing at it. For more resources, I highly recommend the website governmentisgood.com. It gives a very good defense of the institution of government.