According to Pro Football Talk, no players were selected during the first round of the Supplemental Draft.
Here's the order for the 2006 Supplemental Draft, which was scheduled to get underway at 1:00 p.m. EDT.
1. San Francisco
4. Green Bay
7. New Orleans
12. St. Louis
14. New York Jets
16. San Diego
17. Kansas City
25. New York Giants
27. Tampa Bay
31. New England
The order is determined via a weighted lottery based on the 2006 draft order. For each round, teams have ten minutes to decide whether to use a pick on a player. If two teams or more teams put in a claim on a player in a given round, the team with the highest priority gets the player.
The player most likely to be selected is former Virginia linebacker Ahmad Brooks. Since the 49ers have first priority and are one of the teams believed to be most interested (indeed, San Fran coach Mike Nolan was the only head coach present for Brooks' Pro Day workout), a team like the Giants or the Dolphins will have to predict when the Niners would make a move, and jump on Brooks one round earlier.
Using a pick in the Supplemental Draft results in a forfeiture of that pick in the April 2007 draft. Also, the team using a pick in a given round must actually hold the rights to the pick -- if the pick has already been traded away in a given round by the team, the team can't use a pick in that round for the Supplemental Draft.