President and Mrs. Reagan attended church services in this mountain hamlet today and afterwards stopped to chat with an elderly family whose plight is at the center of the debate over Reagan's federal budget cuts.

The gray-shingled, stark, American Gothic house of the Farmer family sits directly across from the church, and the Reagans stopped to talk with Dora Farmer, 88, and her daughter, Princess Caldwell, 71, and son, Finley Farmer, 61, who were sitting on the front porch.

Caldwell later told reporters she "draws a little Social Security" and some supplemental benefits--"but not much"--because of her diabetes. Her brother said he is out of work but is in a training program to learn how to operate heavy equipment.

But they did not think to tell the president about these problems. In fact, they were so excited about the president's sudden appearance on their front porch, Caldwell said, that she did not remember what they had talked about.

"I swear I was excited. I never talked to a president before and you-all'll have to understand," Caldwell said as cameras whirred and the family attempted to field a volley of questions from traveling White House press corps. "I didn't think he would be that friendly."

The Reagans, in Tennessee for the opening of the world's fair in Knoxville, were the weekend guests of Senate Majority Leader Howard H. Baker Jr.--or as he is known more familiarly here, "Howard Henry."

At the plain and simple First Presbyterian Church, which Baker attends when home, the pastor, the Rev. Charles J. Boonstra, said the Reagans' attendance was a "tremendous honor" but he did not alter his services because they were there. He acknowledged their presence and offered a "blessing" for them, and then went ahead with the weekly special part of the service called "the message to the children."

Calling the children down to the altar, he used a potato to illustrate a story about an imaginary family by the name of "Tater." Their bossy father, "Dick," Boonstra said, was always telling everyone what to do; the cantankerous mother, "Aggie," was always causing trouble.

Then there was a daughter "Imma" who copied everyone, and another, "Irri," who always needled. Brother "Hezzie" could never make up his mind and "Speck" would always hide in the corner and wait for others to go first.

But there was a daughter named "Sweet" who was the "peacemaker and love giver." Which one of these taters would you want to be like, Boonstra asked the children.

"Sweet Tater," they all yelled.

At the close of services the Reagans joined the congregation in singing a hymn to peace, "In Christ There Is No East or West." Reagan put on reading glasses and Mrs. Reagan put her arm around his waist.

Baker, who provided the two-bedroom timber and stone guest house overlooking the New River and Cumberland Mountains for the Reagans, said he and the president had a "little bit" of an opportunity to talk about the budget stalemate. The president talked this morning with Secretary of State Alexander M. Haig Jr. about developments in the Falklands.

But Baker said that mostly he had attempted to provide a relaxing atmosphere for the president. After Reagan's speeches at the fair's opening on Saturday, Baker threw a barbecue at his home with singer Dinah Shore and guitarist Chet Atkins. Tennessee Gov. Lamar Alexander also entertained, playing everything from Chopin to Hank Williams songs on the Bakers' piano.

The Reagans returned to Washington this afternoon.

Baker said of the president, "I think he enjoyed most not having anything to do. We left him alone for three hours and he acted like it was the greatest gift man could bestow."