Gabrielle Giffords was gunned down along with 20 other people on Saturday morning during an event in her constituency.
The shooting sent shockwaves across the US, and Prime Minister David Cameron yesterday sent a message of support to the American President.
Last night medics said Mrs Giffords was able to squeeze hands and show two fingers, something trauma surgeon Dr Peter Rhee said was "about as good as it is going to get."
"When you get shot in the head and the bullet goes through your brain, the chances of you living is very small and the chances of you waking up and actually following commands is even much smaller than that," he said.
The medical prognosis came as authorities investigated the motive of a gunman in the attempted assassination of the Democratic member of the House of Representatives.
Mrs Giffords was shot while attending an event at a busy supermarket in Tuscon, Arizona, an attack which also resulted in the deaths of a federal judge, nine-year-old Christina-Taylor Green, granddaughter of Dallas Green, the former manager of the Philadelphia Phillies baseball team, while injuring a further 13.]
Authorities said Mrs Giffords was targeted by a man with a semiautomatic weapon outside the supermarket. Police in Arizona have the suspected gunman in custody, a man identified locally as 22-year-old Jared Loughner.
Loughner was described by Pima County Sheriff Clarence Dupnik as mentally unstable and possibly acting with an accomplice. His office said a man in his forties, thought to be in an associate of Loughner, was photographed by a security camera near the scene and was now wanted for questioning.
Mr David Cameron expressed his shock at the assassination attempt in a message sent to US President Barack Obama, saying that "violence and hate" must not be allowed to stifle political debate.
"That such an attack should have taken place against a member of Congress as she was meeting her constituents in a shopping centre on a Saturday morning is especially shocking to all of us who believe in democracy," he said. .