Every time new numbers came into the Minnehaha County Courthouse in Sioux Falls Tuesday night showing Republican Sen. James Abdnor widening his lead over his challenger, Gov. William J. Janklow, a cheer went up from supporters of Rep. Thomas A. Daschle (D-S.D.).

The premise of Janklow's campaign was that he would be a stronger candidate against Daschle, who was unopposed for the Democratic nomination for Senate, and South Dakota Democrats emphatically agreed. The bad news for them, however, was in the state's gubernatorial primaries.

State Rep. Lars Herseth won the Democratic gubernatorial nomination in an upset of former governor Richard Kneip, who was considered the party's strongest candidate in November. The Republicans nominated former House speaker George Mickelson, considered a fine campaigner and who ran, one observer said, "a flawless campaign."

The South Dakota results are a rough microcosm of the results of the 20 primaries held so far, beginning in Illinois on March 18. Eight states held primaries Tuesday, and North Carolina held a runoff.

Democrats appear at this point to have strengthened their drive to regain control of the Senate, while Republicans seem to have made themselves stronger in the gubernatorial races.

The California Republican Senate primary is an exception to this pattern. Rep. Edwin V.W. Zschau, a moderate considered the strongest potential challenger to the vulnerable Democratic Sen. Alan Cranston, won the 13-candidate primary with 37 percent of the vote. Conservative television commentator Bruce Herschensohn of Los Angeles was second with 30 percent.

Iowa Gov. Terry E. Branstad, plagued by farm-economy problems, will face former state Senate majority leader Lowell Junkins, who defeated Lt. Gov. Bob Anderson by 20 points. Republicans predict a "real horse race," in the words of Rep. Thomas J. Tauke.

"That's going to be a toughie," said Michele Davis, executive director of the Republican Governors Association. "Governors have a tendency to be held to blame for problems." Iowa Republicans said they think Branstad may have gotten something of a break, however.

"The opinion polls and Republican observers arrived at a consensus that Anderson was a better challenger," Tauke said.

Sen. Charles E. Grassley (R-Iowa) was unopposed for renomination and is heavily favored over Des Moines lawyer John Roehrick.

The primary results so far appear to have boosted GOP prospects for picking up Democratic governorships in Texas and New Mexico and holding GOP governorships in South Dakota, California and Illinois.

Former assistant interior secretary Garrey E. Carruthers, who topped a field of six in the New Mexico primary, "totally wrapped himself in Ronald Reagan and won decisively. That has to be good news for Republicans everywhere," said Davis. He will face Democrat Ray Powell, a businessman in his first run for office, who defeated two write-in candidates.

Democrats now hold 34 governorships and the Republicans have 16. The Republicans have a 53 to 47 majority in the Senate.

The primary results seem to have improved the Democrats' prospects of picking up the Republican Senate seat in Alabama as well as in South Dakota.

In the Alabama Senate primary, Rep. Richard C. Shelby, a conservative Democrat, avoided a runoff by defeating Jim Allen Jr., son of the late senator, by a 52 percent to 35 percent. He will meet Sen. Jeremiah Denton, a vulnerable conservative freshman.

"The polls indicate that Shelby is only about 4 to 9 points behind Denton, which is striking distance," said campaign consultant Bob Squier.

In the race to succeed Gov. George C. Wallace, Lt. Gov. Bill Baxley, a liberal populist, was forced into a runoff with Attorney General Charles Graddick. Baxley won 36 percent to Graddick's 30 percent, but a poll last week by the Birmingham News showed him favored over Baxley in a runoff.

In other races:

*New Jersey: House Judiciary Committee Chairman Peter W. Rodino Jr. easily defeated Donald M. Payne, a Newark city councilman who hoped to become the state's first black congressman.

*Mississippi: Attorney Mike Espy, hoping to become the state's first black House member since Reconstruction, narrowly missed receiving 50 percent of the vote and was forced into a runoff with Pete Johnson, whose grandfather and uncle served as governor. The winner will meet GOP Rep. Webb Franklin.

*Iowa: Fred Grandy, who portrayed "Gopher" on "The Love Boat" television series, won 68 percent of the vote for the GOP nomination for the seat of retiring Rep. Berkley W. Bedell (D). He will face Clayton Hodgson, a former Bedell assistant. David Nagle, a former state Democratic chairman, defeated state House majority leader Lowell Norland and will battle state Rep. John McIntee for the seat of retiring Rep. Cooper Evans (R).

*South Dakota: Restaurant owner Dale Bell won the Republican nomination for Daschle's at-large House seat, and will face state Sen. Tim Johnson, a Democrat.

*North Carolina: Former Shelby mayor Lester D. Roark won the runoff for the Democratic nomination for the House seat being vacated by Rep. James T. Broyhill, the GOP Senate candidate. He will face Republican state Sen. Cass Ballenger.