Basically, conservatives have been split on this issue. Many supported it on the grounds that it was enforcing "individual responsibility", although others correctly opposed it as an infringement of individual freedom. Over time, many former supporters did eventually change their minds. Others, like Ann Coulter, now seem to favor it -- at least if imposed by state governments rather than the federal government.
Roy's piece is long, but worth reading in its entirety.
I wrote about the problems with the pro-mandate conservatives in this piece for the Fall 2008 issue The Objective Standard, "Mandatory Health Insurance: Wrong for Massachusetts, Wrong for America":
Nor does mandatory health insurance promote "personal responsibility," as [some] conservatives claim.
Personal responsibility presupposes that an individual has the freedom to make his own decisions and enjoy (or suffer) the consequences thereof. Personal responsibility presupposes that if a patient wants to pay a willing insurer more money now in exchange for the assurance of lower future costs if he becomes ill, then he is free to make that choice.
Similarly, personal responsibility presupposes that if he chooses not to purchase health insurance and later incurs a $10,000 medical bill, he will be held accountable for it even if he has to sell his car, borrow money from his family, or rely on charity. When the government forbids an individual from making such choices about his health insurance, it makes personal responsibility in this area impossible.