Attorney Barry Levine accused government of lawyers of fear-mongering by opposing Hinckley's request on grounds he remains a danger to the community.
Hinckley wants a federal judge to allow him to take four-day, unsupervised visits every two weeks to his parents' home in Williamsburg, Va., about three hours south of the nation's capital.
Over the past year, reports CBS News Correspondent Stephanie Lambidakis, Hinckley has left St. Elizabeths Hospital in Washington on six day-trips and two overnight stays, and because those visits apparently went well, Hinckley's lawyers are asking for considerably more freedom.
"It is undisputed that not a single negative occurrence took place" during the shorter visits, Levine argued at the start of a hearing expected to run two days.
In court filings, government lawyers reminded the judge that in trying to kill Reagan — an attempt to impress actress Jodie Foster — Hinckley shot three other people, including James Brady, who was permanently disabled and has been confined to a wheelchair ever since.
Hinckley has lived at St. Elizabeths since he was acquitted of the shootings in 1982 by reason of insanity. Since then, doctors say he has made substantial progress, and his attorneys told the court he has proven that he poses no danger to himself or others.
Their motion is part of an incremental effort they hope will eventually allow Hinckley to leave the hospital and live full time with his family. His attorneys say he will spend the time away from the hospital looking for work and education opportunities "so that he can work towards becoming a productive, self-sufficient member of society."
"It is important to start this transition and allow Mr. Hinckley to begin to integrate himself into that community," his attorneys wrote the court.
Last December, U.S. District Judge Paul L. Friedman allowed Hinckley limited unsupervised day trips with his parents, though he rejected his request for longer, extended visits to Williamsburg.
Since late last year, Hinckley has had six of these day trips in the Washington area, and has stayed overnight with his parents in an area hotel on one occasion, his attorneys said.
They said he visited restaurants, shopping malls, museums and a movie theater, all without incident and without anyone recognizing him.
Government attorneys counter that Hinckley has been deceptive about his relationship with a former girlfriend and is not ready for the unstructured trips he seeks. If his request is granted, they said, he will be allowed to "roam at will over an undisclosed distance for anything he deems related to vocational or educational pursuits."
His involvement with Leslie DeVeau, the former girlfriend, is "disturbingly unclear," the government lawyers told the court. They said he calls her twice a day when not on supervised release and hopes for a relationship in the future. DeVeau, they said, would not be interviewed about their relationship under appropriate conditions.
The Reagan and Brady families strongly objected to Friedman's ruling last year granting the unsupervised visits.
"It's outrageous I think to all of us that somebody who would try to kill the leader of the free world, who happened to also be my father, wounded the people that he wounded that day, March 30, 1981, would be able to finally be freed to have these unsupervised visits," said Michael Reagan on CBS News' The Early Show last year.
Reagan told co-anchor Hannah Storm that Hinckley poses a threat to the general public if he goes off his medication, and expecting his elderly parents to monitor him is unreasonable.
"I mean, here's a man who has fooled many people during his lifetime, he's written in his diaries he's able to fool psychiatrists," Reagan said.
Reagan also said Hinckley has never taken responsibility for the shootings.
"Here's a man who says 'I'm fine, let me have a few days with my parents' who has never apologized to those people that in fact he shot at and hit," he said.
All of Hinckley's trips off hospital grounds have been conducted under surveillance by the Secret Service, and his lawyers said Hinckley would not object to the Secret Service alerting local law enforcement authorities of the visits.