Early Tuesday evening, the election broadcast team at CBS television excitedly projected the upset defeat of freshman Rep. John P. Hiler (R-Ind.).

ABC was on the air saying its exit polls showed Democrats would pick up 30 seats. CBS early on was foreseeing a 35-seat gain for Democrats. NBC began at 26, but altered its numbers during the night.

Late last week, the venerable Gallup Poll put a wet finger to the wind and projected a Democratic surge in the House that translated to a pickup of 33 seats. The Chicago Tribune's final weekend poll had Illinois Gov. James R. Thompson (R) with a 15-point edge over challenger Adlai E. Stevenson III (D).

Republicans drooled at the prospect of winning a new U.S. Senate seat in Mississippi. One GOP pollster was privately predicting defeat for Democratic incumbent John C. Stennis as his "upset of the year." Another put the challenger within eight percentage points of Stennis.

Now, in the reflective calm of the morning after, one thing is plain. None of it happened that way.

The Democrats picked up 26 House seats. Stevenson and Thompson were neck-and-neck, with the race still undecided yesterday. Stennis was reelected with a remarkable 64-to-36 edge. CBS, before Election Day was history, ended up apologizing when it became clear that Hiler was going to win.

Candidates, television and radio networks, newspapers and magazines pay many millions of dollars every election year for the kind of public opinion research, not infrequently errant and misleading, that voters were served up again this fall.

"You want to know what the outcome is," said William R. Hamilton, one of the leading Democratic pollsters. "It's the next best thing to the National Football League when you don't have it."

Richard Wirthlin, the private pollster for President Reagan, is quoted as calling it "the best, ABC science. Almost Being Certain."

But it is right often enough, and often astoundingly so, that polling and projecting have become important forces in the political process. And so it was in the 1982 elections. Many projections were right on or near the money; many others were dreadfully off.

It's all very mysterious, as Sen. Bob Packwood (R-Ore.) seemed to be saying yesterday. He told reporters that GOP weekend polls had most Republican Senate incumbents winning by 10 to 12 percent. Then, he said, there was a sudden and inexplicable drop to 2-to-3 percent.

Said Patrick Caddell, who was Jimmy Carter's poll-taker: "Some of these candidates got very late surges, and you just don't pick that up in the polls." Caddell claimed to have detected such a late surge, although it was not enough to win, for Lewis E. Lehrman in the New York gubernatorial race.

Another Democratic pollster, Peter D. Hart, said, "The two biggest upsets of 1982 were the Pennsylvania and Illinois governorships, not because an underdog won, but because they were so close . . . . You had states that were hurting, popular governors faced with discontent and that discontent wasn't reflected in the polls."

Hart's own projections were a 23-seat gain for Democrats in the House, a two-seat gain in the Senate and a pickup of six governorships. He was low on the House figure, there was no Senate change and Democrats gained seven governorships.

"As I've said, anybody can hang up a shingle and get into this business," he added.