The Catholic Church explicitly rejects single-issue voting.
Not all Catholics do, however. Sr. Joan Chittister, for example, adding single-issue voting to the list of topics about which she considers herself wiser than the Church, advocates voting on the single issue of aid to the poor, and other progressive Catholics aren't real certain why that's wrong.
But of course, "single-issue voting" plus "American Catholics" far more often adds up to "abortion," or more generally "right to life."
What the Church teaches is that the right to life (with new facets of it made explicit as new ways of offending against it are dreamed up) is the primary political issue, but far from the only political issue. Many pro-life Catholics don't like the way this teaching is abused -- by, for example, Sr. Joan Chittister -- to assert a moral equivalence between the right to life and other, lesser issues.
The fact that it is abused, though, is not a reason to conceal the teaching. The Church can't say, "The right to life is the one issue a candidate must be right on. We have no further comment until there are enough pro-life candidates."
And it's not only a matter of teaching the truth that there are right and wrong positions on issues other than the right to life. It's also a matter of politics.
Catholics need to know what is, as well as what ought to be. And what is, in the United States, is a marketplace of political ideas, of ideas on what which level of government should and shouldn't do. What is is that ideas about issues other than the right to life are being proposed, debated, evaluated, accepted, and acted upon.
A rightly-ordered concern with the primacy of the right to life cannot ignore what is. The Church cannot remain silent on other issues until and unless the country accepts what the Church says about the right to life. Catholics have an obligation to participate in the political life of their society. To meet this obligation, we have to participate in the political life as it exists, not as we want it to exist.
My point is narrow: It's wrong to criticize Catholic statements on politics for mentioning issues other than the right to life. Particular statements may be criticized for muddling the issues, but not simply for mentioning them. To do so is to fail both politically and morally(!); politically because you'll never get what you want if you don't tell anyone what you want; and morally because you have an obligation under justice to contribute to the common good by promoting Church teaching on the issues to the body politic.
[And yes, of course specific personal obligations under justice will vary; that's what makes them personal.]