In response to yesterday's ruling the owners asked for a stay while they appeal the ruling. Judge Nelson asked the players to respond, and they have asked Judge Nelson to order the owners to immediately start the league year. Nelson is giving the owners until 5PM tomorrow to respond. We don't know whether Nelson will indeed force the owners to start the league year if they do not do this voluntarily, but it seems likely.
It's likely that all sides are trying to figure under what rules the doors will open. Right now players are allowed in the buildings, but not much more than that - they're being denied access to training rooms and can't do much in the building right now. Free agency and salary cap rules are also relevant, and although it's been reported that the league will open for business under 2010 rules if they're forced to, the players will likely find those rules too restrictive and this could be used against the NFL in a court of law.
In any case, Judge Nelson should rule on the stay of the injunction sometime tomorrow evening or afternoon. Per Andrew Brandt, if the stay is not granted the NFL will appeal with the Eighth Circuit asking for an immediate stay of the injunction. This could take a couple of days, so it's unlikely we'll see free agency or player trades before the draft.