According to the Daily Mail, Medley, 23, was shot in the eye by gunman James Holmes during the shooting at a screen of "The Dark Knight."
According to CBS News, Medley's family has been told that his medical bills could cost up to $2 million if he fully recovers. His wife, Katie, gave birth to their son, Hugo Jackson Medley, in the same hospital on Tuesday.
Though Medley's condition is still critical, his brother, Seth, said he is showing small signs of improvement.
"There are indications that he understands us and can tell who we are," Seth said to ABC News. "His wife talks to him and he shutters. There are obvious signs he understands."
According to Seth, the doctors call his brother's small successes (a thumbs up on command and a clenched fist), "purposeful movement."
Medley's longtime friend Michael West is trying to raise money to help cover the cost of the medical bills.
"Caleb, he doesn't have any insurance so I put together a website," Michael said, adding that Caleb was looking forward to being a dad. "We've talked to him because we know he can hear us. He needs to get better because he needs to be a dad."
There is also a Facebook page dedicated to Medley's story.
The website had raised $70,000 thus far, the Associated Press reported. According to Think Progress, The Affordable Care Act, which the Supreme Court ruled constituational last month, would extend health insurance to up to 30 million of uninsured Americans like Medley. The act will not be fully implemented until 2014, the Huffington Post reported.