The division between positive and negative rights was created by libertarians and is generally only used in libertarian propaganda. One of the problems with that division is that even so-called negative rights still require some form of third-party involvement if they are to be enforced. For example, it is all well and good to have the right not to be brutally beaten to death (a so-called negative right), but if there is no police force to support it then it is not a right in any practical sense. So, while it may be possible for certain rights to be negative in theory, for such rights to be effective in practice (that is, for such rights to be respected) they require the actions of enforcers and are therefore positive rights.
I think that what motivates libertarians for the most part is the desire to avoid paying tax (and I declare straight away that I have little sympathy for this position). In order to justify this position, they invent a division between those rights that can only be supported by state spending and therefore taxation and those rights which (in theory) do not require state spending. They then use this to mount an argument that the only true rights are negative rights and that taxation is somehow immoral.
I think that this argument is complete and utter rubbish. I believe that all people do, in fact, have the right to equitable access to medical treatment, to education, et cetera. I believe it is wrong for a person to be given or denied medical treatment just because of how much money they have. Furthermore, I believe that each member of society has a responsibility to all of the other members of society. Everyone (including libertarians) reaps the benefits of living in our society and with these benefits come responsibilities. Those who live within our society but refuse to pay tax are not being ethical and high-minded, even if they do not access services that are paid for by taxation - no, they are leeches. The only way that a person can justify not contributing to society is by leaving society. If libertarians really don't want to pay tax then they should go and live in a cave somewhere and withdraw from society completely.