On Tuesday night, Jane Palazzolo woke to a telephone call from her only son, Terrence Patrick Daly, a 21-year-old Army air traffic controller trainee stationed at Fort Bragg, N.C.

"They're shipping me to Grenada," he said, carefully making his voice sound strong and normal, she recalled. He added: "They've given me a flak jacket, a rifle and 100 rounds of ammunition."

Palazzolo had a hard time getting back to sleep that night and since then she and her husband Brian have told congressmen, senators and newspapers that they don't like what is happening in Grenada and Beirut.

Last night, crowded on to a comfortable couch in their Alexandria town house with their 10-year-old daughter, they carefully watched President Reagan's televised speech and it didn't change their minds.

Their eyes rolled when the president mentioned the strategic importance of Lebanon. Brian Palazzolo snorted skeptically when Reagan spoke of efforts to minimize casualties.

When it was over, Brian Palazzolo, a Vietnam veteran and Patrick's stepfather, said: "Well-scripted, but this is what starts wars. They explain why we're in there and then. . . they say we can't leave now and let down those gallant boys who sacrificed their lives. That's what they said in Vietnam, too."

The Palazzolo's, who describe themselves as politically "disenchanted," say they believe that the United States should be calling men and women to arms only if the security of the country is at stake, and they do not believe that is the case in either Lebanon or Grenada.

"There's a lot of communists in the world and you can't kill them all," said Brian Palazzolo. "And you can't sit there and bring peace. You can't cram peace down someone's throat."

Both said they could live with their son Patrick and other young men going to war to protect this country or his family but not, they said, for Lebanon and a tiny Caribbean island twice the size of Washington.

But mostly they said they are worried about whether Patrick will return soon and safely to them and his 19-year-old wife and infant daughter to finish the 2 1/2 years he has to go on active duty. Their son enlisted 15 months ago to get the technical training to become an air traffic controller.

"When he called he said, 'I'm going to be in the bushes monitoring aircraft,' and all I could think of was Cuban snipers and he's out there in the bushes," said Jane Palazzolo. She told him "hang in there" so he wouldn't know how upset she was, but after he called, she said, "I sat here and smoked a couple of cigarettes in disbelief and tried to think about other things. I thought, well there's nothing I can do."

She said she did what she could the next day, starting small--at Alexandria City Hall--and working her way up to the offices of Virginia Sens. John Warner and Paul Trible to register dissent and try to find out what the Army had done with her son. Officials at Fort Bragg have declined to say whether any troops have been sent to Grenada, calling it classified information.

Since then she and her husband have been rising early to watch the morning news, keeping their car radios tuned to all-news stations and coming home in the evening to catch the late news. When any newscast mentions the word Grenada they fall silent and hush their daughter Angela. News of casualties or men wounded last night drew worried looks.

"I can't really adjust to having to look for him coming off one of those planes," said Brian Palazzolo as the first television footage from Grenada flashed on the television.

When Reagan last night mentioned the case of a severely injured marine writing "semper fi" (for semper fidelis, the Marine slogan that means always faithful) for the head of the Marine Corps, Brian Palazolla turned to his wife. "That gets to you emotionally, but if you're one of the guys it doesn't mean very much," he said.

"Or if you're one of the parents," she replied, softly and almost to herself.