The Reagan administration wants to cut in half the federal program that Barbara Harmon-Schamberger says helped her go from a home without running water and electricity to Oxford as a Rhodes Scholar.

The 23-year-old woman, in passionate testimony before a Senate subcommittee last week, said that the program works and the federal investment pays off. "Five years ago," she said, "my highest aspiration was a steady paycheck from any reliable source -- honorable, illegal or otherwise. My only goal: to stay off food stamps. My world views were limited to country boundaries . . . . West Virginia's last Rhodes Scholar was the son of a governor. I, their newest, am the daughter of a welfare mother."

The program Harmon- Schamberger credits with lifting her aspirations is Upward Bound, one of several aimed at encouraging disadvantaged students to finish high school and college. The Senate subcommittee on education, arts and humanities held hearings that focused on funding for so-called Trio Programs, a group of five federal programs that offer support services to low-income, first-generation and physically handicapped college students.

As Sen. Claiborne Pell (D-R.I.) leaned over to catch every word, Harmon- Schamberger explained that not only had she often gone to bed hungry, but also her home lacked even the basic amenities. "Until recently we did not have adequate heat," she said, describing how her family's clothes froze solid in a chest of drawers. The daughter of a white mother and a black father, Harmon-Schamberger said she had been abused and rejected by both blacks and whites. "For 13 years it was drummed into me that I couldn't succeed. I was never a good student." Her mother, who encouraged her to become a voracious reader, was her only supporter.

Then just when she was drowning in a sea of problems, Upward Bound became a life raft of opportunity by providing counseling, financial aid and academic training. She flunked 11th grade for health absences, and wanted to quit school. But a caring, perceptive Upward Bound guidance counselor spotted her talents and challenged her to use them.

" He pushed, conned, cajoled and all but blackmailed me into staying in school," she testified. As she neared graduation, her counselor's wife insisted that she attend West Virginia University. "When I asked her why, she said, 'Because you're going to be Upward Bound's first Rhodes Scholar.' " Harmon-Schamberger had never heard of the academic honor and thought Oxford was "somewhere near Harvard."

She graduated with a quadruple undergraduate major in political science, history, English and international studies. She plans to study international relations at Oxford University, which she leaves for in a few days.

In introducing her to the subcommittee last week, Sen. Jay Rockefeller IV (D-W.Va.) noted she was the 20th West Virginian to win the honor and the state's first woman. In urging his colleagues to ignore the Reagan administration's proposal to halve the $175 million program, he called such programs "critical" because "every young American who wants a college education ought to have the chance. It is my hope that Barbara will go into politics one day."

Harmon-Schamberger said it is indeed her ambition to be a U.S. senator, and she gave a foretaste of an attribute that could be a political asset as she laid aside her written testimony and spoke from the heart: "When I start feeling worried, I remember that I'm a Rhodes Scholar. How I got there was Upward Bound. It's the confidence level that changes everything."

It would be easy to say that Harmon-Schamberger is a fluke because out of 3 million participants in the Trio programs, she's the first to attain a goal so exalted as a Rhodes scholarship. But there are countless other examples of people who are moving along similar lines of excellence. Said Harmon- Schamberger: "I guess my story could bother people because it means they have a responsibility. Just because you're poor doesn't mean you can't accomplish. It's about access and opportunity."