President Reagan's life may have been in graver danger after he was shot in the chest Monday than was evident from preliminary medical reports.

The president might have died of blood loss and shock if Secret Service agents had ordered him transported to a more distant hospital, such as Walter Reed Army Medical Center or Bethesda Naval Hospital, rather than driving him swiftly to nearby George Washington University Hospital, according to medical sources familiar with his case.

Jerry Parr, the agent who dove on top of Reagan after pushing him into his limousine, noticed a trickle of blood coming from the president's mouth, the first clue that he had been shot, moments after the car sped away from the Washington Hilton Hotel, according to Treasury Secretary Donald Regan. Parr, who had ordered the car to return to the White House under the assumption that Reagan wasn't shot, then diverted it to the hospital.

A D.C. paramedic noticed blood on Reagan's face when he was brought into the emergency room -- well before the White House confirmed that he had been hit.

A doctor who was present confirmed yesterday that about two quarts of the president's blood -- between one-third and one-half of his total blood volume -- flowed "at a rather brisk rate" out of the left side of his chest as soon as the tube was inserted between the chest wall and his collapsed lung.

Medical sources also said he initially showed some heart irregularities, and the surgical intern who treated him, Dr. William O'Neill, told a New York Times reporter that the president's blood pressure was only 78 -- low enough to signal impending shock.

Reached yesterday, O'Neill declined to comment further on Reagan's vital signs when he was first examined. Other doctors at the hospital said his; blood pressure may have fallen briefly, but within a few minutes rose to a normal level of 120. They said reagan was never actually in shock, a condition in which blood pressure falls so low that the brain and vital organs are receiving insufficient blood.

But in the opinion of Roberto Hernandez, a D.C. paramedic who helped; carry the stricken president into the emergency room, Reagan looked like a man whose life was in danger.

Hernandez was coming out of the hospital as Reagan was being helped out of his limousine by two Secret Service agents.

"When I saw him it just shocked me," he said. "I noticed he looked very pale, and he had an apprehensive look . . . . The stare in his eyes was like he was in a slight daze."

"He looked like he was in shock," Hernandez said, and his first thought, knowing Reagan's age (70), was that he had suffered a heart attack.

Then as the group passed, "Reagan's eyes rolled upward, his head went back, his knees buckled and he started to collapse," Hernandez recalled.

One agent called for help. Hernandez grabbed Reagan's legs and helped carry him into the resuscitation area of the emergency room.

"He was gasping for air. He was breathing kind of deep," he said, demonstrating by making a choking sound. As they placed Reagan on the stretcher, "he turned in my direction and said, 'I can't breathe.'"

At that point, Hernandez said, he noticed a little blood around Reagan's nose, but did not see any as his clothes were removed.He said he heard one of the agents tell a doctor "we don't think he has been hit. We think he may have broken a rib when we pushed him into the car."

A surgeon who saw Reagan minutes after his arrival said he remained conscious but was having obvious difficulty breathing. "He did have a couple of quarts of blood there" in the left side of his chest, pressing on the collapsed left lung, he said.

"When he was lying down, it didn't seem he was in extremis . . . ," the doctor said. The president could not have been safely transferred to another hospital, however, he added.

Dr. Joseph M. Giordano, the head of the hospital's trauma team, who first saw the president five minutes after his arrival, said that by that time his blood pressure was returning to normal, but that his breathing problems and signs of blood loss made it necessary to insert a tube into his chest to reinflate his lung before an X-ray could be taken.

As soon as the tube went in, according to another surgeon present, they drained more than two quarts of blood. Doctors immediately administered intravenous fluids and ordered a transfusion. Reagan received five units of blood -- about 2 1/2 quarts -- before being taken to surgery.

Giordano said that only 15 percent of patients with wounds such as Reagan's ever need surgery. In most cases, he said, a chest tube connected to a suction device drains blood and air, allowing the collapsed lung to reinflate. Surgery is done only when blood continues to flow from the tube, indicating possible life-threatening damage to the heart or a major blood vessel.

Since his operation, Reagan has improved steadily, and a statement yesterday said he was in good condition despite some pain requiring mild medication -- normal for someone who has had major surgery. He was walking around, eating solid food, and last night was expected to receive his last dose of antibiotics (given after surgery to prevent infection), according to a doctor.