Jennings Randolph, one day shy of 79, is a man easy to underestimate. He has served in Congress almost 50 years, and looks almost like a caricature of a senator. His nickname is "Fats." His eyelids are heavy like a turtle's: his jowls thick and flabby like a bulldog's.

But the West Virginia Democrat, the last of the New Dealers, showed yesterday that there is still fire in his ample belly as he rose to defend two of his favorite programs -- the Appalachian Regional Commission and the Economic Development Administration.

The Reagan administration is trying to kill both programs, vestiges of Lyndon B. Johnson's Great Society, as part of its budget-cutting effort.

Randolph made it clear from the start where he stood on the issue as hearings on the programs opened in the Senate Environment and Public Works Committee. Misquoting Mark Antony, Randolph declared: "I come to praise Caesar, not to bury him. I come to praise these agencies and the work they've done, not to bury them."

For the next hour, his voice rose and fell like the West Virginia mountains, flowing as smoothly and as dangerously as hill country moonshine. His right fist hammered on the table. His deep brown eyes flashed. A quarter-century seemed to fade from his face.

He cited all the proper authorities necessary for a politician: his grandfather, God and a couple of academic studies. "I sought to hear the voice of God, and I climbed the highest steeple," Randolph said. "But God declared, 'Go down and dwell among the people.'

"I dwell among the people. And frankly, it is my responsibility to speak for the people."

Randolph, longtime chairman of the committee, authored the legislation creating both agencies. But with the Republican takeover of the Senate this year, he finds himself in the unusual position of being in the minority, his committee in the hands of Republicans.

But with freshman Sen. Frank H. Murkowski (R-Alaska) chairing yesterday's hearings, Randolph was able to dominate the first 90 minutes, reminding Murkowski at one point, "This committee has been very considerate of the needs of Alaska over the years."

The Republicans offered little in defense of Reagan's proposal to put the Appalachian Regional Commission -- a federal-state agency that serves 13 Appalachian states, including West Virginia -- out of business at the end of this year.

Normally, the commission's federal co-chairman would be the administration spokesman on such issues. But that post is held by Al Smith, a holdover from the Carter administration, and he spent most of his time defending the agency's work.

When Commerce Secretary Malcolm Baldrige arrived 90 minutes late for the hearing, he spent most of his time criticizing EDA and eight other regional commissions that the administration proposes to eliminate.

"Budget reductions are always bitter pills to swallow. However, when considered with the other parts of the president's economic plan, they will result in a healthier and strong economy with reduced inflation," Baldrige said.

Sen. Alan K. Simpson (R-Wyo.) said he couldn't agree more with Reagan's cuts, and he complimented Baldrige: "I think you've hit one of the soft underbellies of the dragon we're suppose to slay."

Randolph asked Baldrige to study his earlier remarks. Then he left for his birthday party.