I have seen the interview that Abp. Burke gave to Kathryn Lopez over at NRO. He makes the following statement:
"If a Catholic knowingly and deliberately votes for a person who is in favor of the most grievous violations of the natural moral law, then he has formally cooperated in a grave evil and must confess his serious sin. Since President Obama clearly announced, during the election campaign, his anti-life and anti-family agenda, a Catholic who knew his agenda regarding, for example, procured abortion, embryonic-stem-cell research, and same-sex marriage, could not have voted for him with a clear conscience."
Abp. Burke is a great legal mind and a truly great Churchman. As he has formulated the matter above, though, there seems to be an element that, while not wrong, is imprecise as a matter of moral theology; I mean Archbishop Burke's articulation of the conditions for formal cooperation in an act. Formal cooperation requires that there be assent to the end, the purpose of the act with which one cooperates.
Perhaps this is what the Archbishop means by "deliberately", but deliberation is not, in the language of moral science, the same as willing(ness).
I might knowingly and deliberately tie up a fellow hostage while the house robber holds us both at gunpoint, without assenting implicitly or otherwise to the act of robbery. I would yet be but a material cooperator. Similarly, a Catholic might have voted for Obama despite the candidate's views on abortion, etc., and still have only cooperated materially in any eventual evil that came about as the result of the implementation of the President's policies. In sum, only someone who voted for Obama because of his abortion policies would be guilty of formal cooperation.
Catholics who voted for Obama despite their opposition to his life policies were appallingly naive and ill-advised. They acted stupidly, but they did not necessarily commit a mortal sin.
In any case, I certainly do not think Archbishop Burke intended his observations to be an armchair condemnation of millions of people - though Tom Peters is using the Archbishop's remarks to Monday morning quarterback the consciences of his fellow citizens and co-religionists.
This is unhelpful, at best.