Rep. Bob Wise, a 35-year-old first-term House Democrat from a West Virginia district that has had four congressmen in three years, welcomes any escape route from obscurity that fate offers. A few days ago, he had one: the momentary fame of being an irritant to Sen. Robert Byrd (D-W. Va.), the Senate minority leader.

The senator was irked that Wise had persuaded the House to delete $26 million for the Stonewall Jackson dam--a bulging barrel of pork in Wise's district. So Byrd personally phoned 124 representatives to convey some down-home praise for the boondoggle. Wise, an Appalachian with a natural story-telling talent, laughingly tells of grateful colleagues thanking him for bringing them to the attention of the great statesman and Senate power Robert Byrd. For those whose arms Byrd singled out for twisting, a word from on high was a high in itself.

For Byrd, the Senate's touch-dial master at reaching out and touching someone, the phoning paid off. In a Senate-House conference committee, he barreled the project through, after having convinced the Senate that this was no time to stop the delivery of pork to the good folks in the mountains, whether they wanted it or not. Ten of 11 House members on the conference committee abandoned the House's opposition to the dam and joined the Senate in approving the project.

It was a loss for West Virginia and the nation. The Stonewall Jackson project would flood 20,000 acres of private land and force some 1,800 citizens from their homes. It was opposed by Wise, the West Virgina state senate, the United Mine Workers Union, several national environmental organizations and the General Accounting Office, which said the long-term numbers on economic benefits and flood control don't add up.

In losing to Byrd, Wise, a former public-interest lawyer who earned $8,100 the year before he won a seat from the Charleston area, may have won much more. There is, first of all, the new respect of his colleagues, who saw Wise break ranks and break tradition in favor of the merits of stopping the dam. "He represents a really refreshing spirit in the House," said Rep. Bob Edgar (D-Pa.). " There are a number of new members willing to take on the system and not be afraid of challenging the conventional wisdom. It's helpful to the House. I liked his courage."

The trait is not new for Wise. As a young lawyer in Charleston, he organized West Virginians for Fair and Equitable Taxation, a citizens' reform group that sought to end the free tax rides given coal and timber companies. He gave legal help to the survivors of the 1972 Buffalo Creek flood disaster, a trauma that still haunts the coalfields.

Wise has a sense of whimsy. It leads him to say that what made him go wrong this early in his congressional career is his friendship with former Rep. Ken Hechler, who served 16 years in the House. Hechler, a populist and then some, rode a rattletrap jeep to visit constituents in the hollows of West Virgina. In Congress, he won laws for black-lung benefits and coal mine safety.

Among other virtues learned from Hechler, aside from the invaluable one of putting the people's wishes before Robert Byrd's, was a taste for the simple life. Wise refused to take the 12 percent raise the House voted itself, and this year he is returning another 10 percent of his salary. At the moment, he is of two minds about getting rid of the money: put it in escrow to be used for charities in his district or just turn it back to the Treasury. Either way, Wise says, "I was better off financially when I was making $8,100. I always had just enough to get by. Now I'm living month to month: two cars, two apartments, and all the going back and forth (to the district)."

Wise's conscientiousness about money has symbolic value. His part of Appalachia is seeing unprecedented suffering because of chronic joblessness. In seven of the 15 counties in Wise's district, unemployment is more than 30 percent. In coal mining, it is 40 percent.

On June 27, Wise organized a congressional forum in which some 20 members stayed late into the evening on the House floor to report on unemployment in their districts. It ran from 28 percent in Laredo, Texas, to 17 percent in Akron, Ohio, to Michigan's 61 percent for black youth. The forum occurred on the same night as Reagan's press conference in which he said the economy is "beginning to sparkle." Wise was breaking ranks again.