At 55, it is likely that Obama's best years are behind him. The Reds do not need to spend big money on a piece that will not be contributing substantially to the next contending Reds team.
The lefty has mounted some decent WARs in recent years, but the Reds don't really have a place for him in the lineup.
Obama is certainly a likable personality, but the Reds can't deny that he is a divisive figure who would draw scorn from a good portion of the fanbase.
As a long-time South Sider, Obama is far more likely to sign with the White Sox.
Obama's number, 44, is already taken by Cody Reed.
At this point in his career, his limited physical agility pretty much restricts him to first base or designated hitter. The Reds have Joey Votto, of course, and the National League doesn't have the designated hitter.
Obama has expressed that after he leaves the White House, he would like to continue working in public service and "probably will not pursue a baseball career." That "probably" does leave the door open a bit, so the Reds should at least make the call. But let's not hold our breaths.
Obama would have to buy a glove first, and we all know how difficult it is to find a left-handed glove. You can't just walk into Wal-Mart and pick one out. You have to order it special.