"It's a one in a million shot," Shaffer said. "You always hope that happens. It would be icing on the cake after a draft like this."
Shaffer had a positive outlook on what most thought was a shallow draft. He said he felt the team did very well.
The White Sox continued taking right-handed pitchers, a trend they began by taking seven righties in the 18 rounds of day one. They ended day two with a total of 16 righties, but only six lefties.
"We need to reload and re-stock our pitching," Shaffer said. "With all the trades in the last five years, we've got to replace those players and get more value back into the system."
Shaffer was especially interested in the Sox 20th-round pick, Wade Kapteyn, a right-handed pitcher out of nearby Illiana Christian High School. Kapteyn's fastball has been clocked at 94 mph and he also has a developing slider and changeup.
After taking two catchers on day one, the Sox took another three on day two in hopes of strengthening a position they are short on in the Minors. They used their first pick of the day in round 19 for catcher Jeffrey Dunbar from the University of California at Riverside. Ironically, Dunbar lists his favorite player as current White Sox designated hitter Jim Thome.
Shaffer listed Dunbar and Kapteyn as top priorities from day two that he hoped to sign.
On day one the Sox took a third of their 18 picks out of high school, but day two saw an almost even split between college and high school players. They took 15 from high school, including six of their final eight picks, and 17 from college.
After right-handed pitchers, the White Sox took the most players at the center field position with six. It's a position that they're currently having trouble filling in the Majors, with Brian Anderson and Rob Mackowiak sharing for the moment.
In the 47th round, the Sox selected Kyle Williams, son of general manager Kenny Williams. The 17-year-old Williams, a second baseman, has received a football scholarship to attend Arizona State University.
"He's a good looking kid and he's got lots of tools," Shaffer said. "He's got a lot of options. I think he'll sit down with his father and weigh those options and come to a decision."
The White Sox first pick, Kyle McCulloch, is a right-handed pitcher from the University of Texas. He was one of their key starters in their championship season in 2005. Shaffer, who was surprised that the Sox were able snag McCulloch with the second-to-last pick in the first round, expects that the Sox will soon sign McCulloch.
"We've followed him for the last four years, and he's dominated his competition every year," Shaffer said. "I think you'll see the fruits of his labor here within the next three or four years."
Shaffer said that he hoped to have a number of players sign with the team in the next several days.
Leslie Parker is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.