It has now been 16 days since Judge Vinson issued his opinion in Florida v. HHS, and the Department of Justice still has not sought a stay of the judgment. This even though Judge Vinson stated that he believed that a declaratory judgment was the functional equivalent of an injunction, at least as applied to the federal government.
One could reasonably surmise that, if DOJ has not yet sought a stay, then it is unlikely to ask for one. Of course, that could change if Judge Vinson enters an injunction to enforce the declaratory judgment--which could happen if one of the plaintiffs believes that the United States is not adhering to the terms of the judgment. But for now, an application for a stay seems unlikely.
As we have discussed before, the federal government's continued implementation of the ACA, even though Judge Vinson declared the entire Act unconstitutional, seems legal; a party does not technically violate a judgment when it takes action arguably inconsistent with a declaratory remedy. But one would have thought that, given several states' stances that they would halt implementation of the ACA, the United States would have wanted a stay if for no other reason than (a) to make its legal obligations perfectly clear, and (b) to alter the status quo, so that the country at large does not come to believe that the ACA is no longer in force.
But apparently the costs in seeking a stay--and there could be several strategic ones, not the least of which would be the implicit admission that the federal government needs a stay--outweigh the benefits, at least in the DOJ's eyes.
P.S. I should also note that the United States has not yet filed its notice of appeal, either. It has until April 2 to do so.