I argue that paying taxes into a "general treasury fund" is not morally objectionable. Jesus was asked about this very thing, and He (Christ) OK'ed payment of taxes, even to the Roman Empire. That suggests that paying taxes, even to Caesar, is not formal cooperation in evil.
However --- and I hope this is a BIG HOWEVER--- paying taxes or making other mandated payments into a fund that is explicitly set up to provide for intrinsic evils, IS morally prohibited.
My argument in more detail, on another thread.
It's a difference between evil-designated funds (HHS) and non-designated funds (U.S. Treasury).
I am saying, refuse to pay for explicitly designated evils (HHS mandate). There's the bright "do not cross" line. AND fight like hell to prevent such things from being funded by the U.S. Treasury.
P.S. Dr. Smith did not spport Obamacare, did not support Obama, and is in fact a major opponent of contraception, sterilization, and abortion, a defender (oftentimes a LONE defender) of Humanae Vitae going back decades, and in general a hero of Catholic philosophy. Though I disagree with her reasoning here, she is trying to find the line between "you must object," and "you mustrefuse."
Do not rashly characterize her as an Obamunist. She is not.
Where I think she goes wrong is that in her effort to want Catholics to be good citizens and not be disobedient to legitimate authority, which would be a sin, she doesn't take serious enough (or creates some sort of moral equivalance) that disobedience to the highest authority would be a mortal sin. And I cannot help but blame the Church a little here by not doing anything serious about Sebelius, ( who is running the whole evil enterprise called Obamacare) and the other abortion promoting "Catholics" who muddy waters in league with the Evil One.
Killing your conscience is the path to Hell.