I think everyone should get basic health care. Does that mean I think we have the right to basic health care? Not necessarily, because saying you have a right to X isn't just a more emphatic way of saying X is a good thing.
Bart Hinkle explains in the Richmond (Virginia) Times-Dispatch:
"Rights summon corresponding and irresistable duties. For instance -- hypothetically speaking -- if receiving timely medical treatment is an inalienable right, and a shortage of nurses and orderlies is causing unacceptable delays, then there would be a social obligation to draft people into service as nurses and orderlies, whether they wanted to become nurses and orderlies or not. Why? Because, as legal theorist Ronald Dworkin puts it, rights are trumps—the demands of rights outweigh all competing demands. But surely people also have a right not to be forced into servitude. So something has to give." (Hat tip to Café Hayek, where most commenters fail to grasp the distinction, perhaps because they oppose universal health care on other grounds already.)
So far so good. But Hinkle and his libertarian buddies aren't content to make a clarifying distinction.
"What has to give is the notion of 'positive rights,' as Isaiah Berlin called them—the right to things, as opposed to 'negative' rights from things, most of which boil down to the same thing: the right not to be messed with. You have a right to freedom of speech, but that negative right not to be messed with while speaking imposes no particular obligation on my part. My only duty is not to interfere with you, which requires nothing. To say, on the other hand, that you have a right to (for instance) housing implies that, if you lack a house, I have an obligation to build one for you, and that if I do not, then I should be made to."
This extension proves too much -- it would lead to the conclusion, for instance, that no one who is arrested should have the right to be represented by a lawyer. Mmm -- might lead to drafting people to be lawyers. Can't have that. How would Mr. Hinkle wiggle out of that one?
(Some references that go deeper are at Wikipedia, including the contention that the distinction between positive and negative rights in general is a linguistic will-o'-the-wisp.)