I'm not sure that's how all libertarians really feel about things. But if it was, it would be a major obstacle to finding liberal/libertarian common ground if libertarians can only be persuaded to care about things that directly affect them. Ignoring for a moment that it's pretty naive to think you're only affected by things that DIRECTLY affect you, talking big about "freedom" and "small government", but only DOING something about it when it benefits you directly comes across as less than sincere.
It's not insincere to focus on the problems that affect you the most and which you understand best. No one can fix everything. We have to choose our battles. Moreover, fixing the problems that affect you the most will make you stronger, and put you in a better position to fix others in the future. If you can eliminate a tax you are affected by, that's that much more money you can spend to support non-property rights if you so choose.
From watching US politics from the outside, it's my impression that libertarians are more likely to take a long-term view and liberals more likely to take a short-term view in some things. For instance, in dismantling a given city program the libertarian might see a future where the city is debt-free and can afford to spend the tax money on useful stuff instead of loan interest, and people previously being employed by the city being employed more productively and thus generating extra well-being around them. In the same situation the liberal might be more likely to stop their consideration at the immediate impact of so-and-so many city workers losing their jobs.
That long-term vs short-term divide explains a lot of the focus on the economy. With many types of problems, every year the problem is not fixed will tend to suck about as much as the last for those affected. That's not the case with the economy and compound interest.
As an example of another long-term vs short-term opinion difference, I'm against "gay marriage" laws, not because I think same-sex unions are wrong, but because I want to take government out of marriage business entirely. Carving new types of marriages in law is to accept that it is the government's business who sleeps with whom. Someone whose relationships also do not conform to the new law will still be left in an unequal, inferior position. For instance, polygamists' unions will not have equal status.