Members of the New York delegation are offering their thoughts and prayers after a gunman opened fire Saturday in Tucson, Arizona, killing at least five people and critically wounding several others, including Arizona Congresswoman Gabrielle Giffords.

The congresswoman remains in critical condition and is heavily sedated at the University Medical Center in Tucson.

The Democrat was greeting constituents outside a Safeway grocery store when a man opened fire with an automatic weapon.

A nine-year-old girl, U.S. District Judge John Roll and Gabe Zimmerman, an aide to Giffords, are among six killed in the attack.

Thirteen people were wounded, including the congresswoman.

Doctors say they are encouraged by Giffords' progress and say she has been responding to their commands.

"When we talk about gunshot wounds to the head, the things that are most concerning to us are if the bullet crosses from one hemisphere to the other, one side to the other, if the bullet crosses through the geometric center of the brain. And I'm happy to say that those were not the case in this instance," said Dr. Michael Lemole, the chief of neurosurgery at UMC Tuscon. "And because of that, Congresswoman Giffords is able to communicate with us this morning through following of simple commands and we're very encouraged by that."

Sources say suspect in custody is Jared Loughner, 22.

A YouTube page linked to Loughner contains several videos that apparently show him talking about government brainwashing, revolution and what he calls the U.S. Constitution's "treasonous laws." One of the videos begins with the sentence "My Final Thoughts: Jared Lee Loughner."

In one video, Loughner describes himself as a military recruit, but the U.S. Army released a statement indicating Loughner was not accepted.

Loughner also had a page on MySpace, but it was taken down after authorities identified him as the shooter. The page included a message with the words "Goodbye friends" and said, "Please don't be mad at me" that was put up just hours before the shooting.

Due to the shooting, the House will suspend all legislative action scheduled for next week.

Calling the shooting "an unspeakable tragedy," President Barack Obama said he dispatched Federal Bureau of Investigation Director Robert Muller to oversee the investigation.

"It is a tragedy for Arizona and it's a tragedy for our entire country. What Americans do at times of tragedy is to come together and support each other," said Obama. "So at this time, I ask all Americans to join me and Michelle in keeping all the victims and their families, including Gabbie, in our thoughts and prayers."

The U.S. Capitol Police is advising members of Congress and their aides to "take reasonable and prudent precautions" about their own security in the wake of the shooting.

House Speaker John Boehner called the shooting an "inhuman act" and said representatives cannot let it deter them from serving their constituents.

"Public service is a high honor, but these tragic events remind us that all of us in our roles of service to our fellow citizens comes with a risk...," said Boehner. "No act, no matter how heinous, must be allowed to stop us from our duty."

Local members of Congress say the security risks are unfortunate but cannot be avoided.

"It just makes you think how many crazy people are in this world, and how unsafe are we all?" said Staten Island-Brooklyn Congressman Michael Grimm. "You don't have to be a public official, It's just that when you are a movie star or a rock star, you're availing yourself to the public more than the average person. So every time you're in the spotlight, you have to worry."

"We all get what we believe to be kook phone calls everyday. So you can't do this job in fear of your life or fear that someone's going to come after you," said Queens Congressman Gregory Meeks.

"A well functioning democracy also requires, I think, that people can talk to their representatives, whether they're in Congress or state legislature or wherever, if they want to and it's important to keep that," said Manhattan-Brooklyn Congressman Jerrold Nadler on CNN. "This entails a certain amount of personal risk I suppose, but I would hate to see a situation where you can't meet with your constituents."

For Congresswoman Carolyn McCarthy, whose husband was killed and son was injured in a shooting on the Long Island Rail Road, Giffords' situation hit home.

"It brings me back to the day of the shooting and killing of my husband and certainly the wounding of my son, who was also shot in the head," said McCarthy. "All I can say was, Kevin was a miracle. They didn't give him any chance to survive and he did. And later on this afternoon, we heard the doctor was very optimistic. And for the doctor to say they're optimistic, I would think she has a very, very good chance of surviving."

Giffords, a former Republican supported President Barack Obama's health care bill, calls herself a "blue dog Democrat," and narrowly won re-election in November over a Tea Party candidate.

Her fellow lawmakers describe her as a caring and wonderful person.

Senator Kirsten Gillibrand, who served in the House with Congresswoman Giffords, released a statement saying, "This hateful crime is a tragedy beyond words. I had the privilege of first getting to know Gabrielle Giffords when we served together on the House Armed Services Committee. More than just a rising political star and phenomenal talent, she is an incredible person. It is an honor to be able to call her a close personal friend. My thoughts and prayers are with all of the victims and their families."

Manhattan-Queens Congresswoman Carolyn Maloney also released a statement which said, in part, "The shooting of Congresswoman Gabrielle Giffords and others, at an event in Arizona designed to serve her constituents, marks a sad day in the life of our nation."

The congresswoman's Tucson office was vandalized after the House passed the health care bill last March and someone showed up at a recent gathering with a weapon.

Giffords was a member of the Arizona House and Senate before heading to Washington, D.C.

Last night, a vigil was held outside the U.S. Capitol for the shooting victims.

Flags on the House side of the Capitol are flying today at half-staff to honor Giffords' aide, Gabe Zimmerman, who was killed in the rampage.