He says Giffords remains in critical condition. She's heavily sedated and he's encouraged about her prognosis. Lemole said he's concerned with three particular issues.
"The first is probably swelling in the brain, something we have a hard time controlling at times," he said.
"The second is more bleeding in the brain. You can imagine if someone punches you in the shoulder you get a little bit of swelling but the next day it starts to bruise. The brain's no different. Bruising is nothing more than microscopic bleeding.
"And the third might be infection because we have pieces of bullet and bone that we don't retrieve and all of those are potential sources of infection, although less than you would think."
There is a team of about 20 or 30 doctors, surgeons, specialists and nurses taking care of the Congresswoman in the intensive care unit, monitoring her around the clock.
In terms of location of the injury, the surgical team tells CBS News that the bullet entered the left read part of the brain, exiting through the front left front part of the brain and miraculously spared any major blood vessels.
Giffords was shot in the head and an aide was killed Saturday when 22-year-oldallegedly opened fire in an area where the lawmaker was meeting with constituents.
The shooting rampage claimed six lives, including a 9-year-old child and U.S. District Judge John Roll, officials said. Thirteen more were wounded at the scene, including Giffords. Five were listed in critical condition and five were in serious condition.