Rep. Gabrielle Giffords is continuing to make progress in her recovery from an attempted assassination Saturday that left six others dead, Tucson University Medical Center doctors said Monday.

Speaking to reporters, UMC chief neurosurgeon Michael Lemole said there had been little change in the Arizona Democrat’s condition, but said that is a positive sign.

“At this phase in the game, no change is good. And we have no change,” he said.

Giffords was shot in the head Saturday morning at a constituent event in Tucson. Six people died and 13 others were injured.

But Lemole cautioned that Giffords, 40, remains in serious condition. “We’re still not out of the woods yet. But every day that goes by we’re slightly more optimistic.”

Lemole said Giffords continues to respond to basic directions but it remains unclear whether her brain injury will affect her ability to speak.

According to her doctors, the biggest concern — as is he case with any gunshot wound to the head — is the amount of swelling to the brain that the victim suffers. Although Giffords has had minor swelling, the risk for damage peaks on the third day, doctors said. That makes Tuesday a significant milestone in her recovery.

If she continues to improve, “We can all breathe a collective sigh of relief after day three,” Lemole said.