I often hear this, but I don't know what it means in practice.
Does it mean that the state views all people as individuals and marriage (or divorce) has no legal effect? I don't see how they can "get out of the "marriage" business all together" without a radical change in the law and culture.
We're rapidly moving towards allowing gays to be married, so I'm not sure how "civil unions for all" is more radical.
Again, marriages are the union of two separate traditions: we have the legal aspect (tax breaks, inheritence laws, automatic rights in emergency situations...etc.), and a separate religious tradition. We've been steadily moving away from the more restrictive aspects of religious marriage--the proliferation of divorce and interracial marriage being two prominent examples--but we still have this legacy of priests having the authority to grant the legal benefits.
Right now the primary legal difference between a civil union and a marriage are federal and interstate laws. Because of the Defense of Marriage Act, same-sex couples cannot receive the federal benefits of marriage, and because not all states recognize same-sex civil unions, they do not travel accross borders.
The only remaining difference is the emotional baggage and religious tradition contained in the notion of "marriage" (set aside, for the moment, the silliness of claims about "traditional marriage").
One way to solve this problem is to pass laws to include same-sex couples within the "marriage" tent. Another solution is to allow "marriage" to be defined purely by religion, and give civil benefits, both state and federal, to anyone who applies.
On a certain level this is a semantic difference. Or, more to the point, for those of us who tend to find religious tradition ridiculous, the notion of "marriage" never held any spiritual or emotional significance, so it doesn't bother us to include homosexuals.
On a Constitutional level, however, this is a conjunction of state and religious function that, while not particularly significant, should be eliminated. The state should remain entirely neutral on the issue of "marriage," recognize none of them, and allow individual churches to decide how their fantasy world will recognize coupling (or polygamist relationships or whatever).