As they gather in Detroit for the preliminaries to their nominating are savoring a new public opinion poll showing the GOP in its most favorable position in at least a dozen years.

The survey, taken in mid-June by respected pollster, Robert Teeter, confirms Ronald Reagan's position as the favorite over President Carter, and shows Republicans nearly at par with Democrats in the congressional races.

It also shows that Republicans are regarded by the voters as the party best able to control inflation, government spending and taxes, to maintain world peace and military security and to assure adequate energy supplies.

Most startling is the indication that in the last six months, as the economy slid into recession, the Democrats have lost a 2-to-1 lead as the party of full employment and are now rated only marginally better than the GOP on the traditional Democratic issue of unemployment.

The survey results are to be made public Monday by Rep. Guy Vander Jagt of Michigan, chairman of the Republican Congressional Campaign Committee, in testimony to the platform committee launching the pre-convention week of activities in Detroit.

Vander Jagt, whose committee paid for most of the survey, which was cosponsored by the Republican National Committee, authorized release of the survey figures to The Washington Post today, with the comment that the results show "the Democrats are as low as the Republicans were in 1974 [the election year after the Watergate scandaal] -- and are going down."

Teeter, president of Market Opinion Research Co. of Detroit, which took the poll, said it points to the possibility of a top-to-bottom GOP victory.

"I'm cautious," Teeter said, "because I've been around long enough to know that in Republican campaigns, what blooms in May and June often wilts in November.

"But the key thing we're finding this year," Teeter said, "is that we've got a very unpopular Democratic president and an unpopular Democratic Congress. The voters really want to change directions, and they know the only way to do that is to vote Repuublican."

He said that situation has not been seen since 1966, when the biggest GOP congressional gain of recent times preceded the recapturing of the White House two years later.

Neither Teeter nor Vander Jagt predicted that Republicans would break the Democrats' 26-year congressional majority. But the current 52-to-48 percent Democratic lead in the poll is less than half the margin Democrats had at the time of the 1978 election and less than one-quarter of the deficit Republicans faced in the Watergate election year of 1974.

As Vander Jagt noted, the Teeter survey shows that Republicans "have gained more in the laxt six months than in the prevlious six years." The gains have been particularly striking in groups targeted in a November Teeter poll that was used in designing the Republicans' $5 million television advertising campaign, focused on the alellged failures of the Democratic Congress.

The survey showed the sharpest GOP gains among young voters, those with high school diplomas, nominal Democrats and residents of the Midwest and South. Republicans have made double-digit gains among all those groups since last fall, and have taken the lead from the Democrats in several categories.

The Teeter poll indicated that Republicans have achieved one of the major goals of the advertising campaign -- increasing the percentage of voters who know that Democrats have long been in control of Congress.

The percentage of those answering correctly which party has controlled Congress most of the time since 1952 went from 68 percent in November to 80 percent in June -- with most of the gains coming among Independents and Democrats.

Among those interviewed, 77 percent agreed that "things have seriously gotten off on the wrong track," and while more people blame that on Carter than did last fall (18 percent vs. 12 percent), even more -- 31 percent now vs. 23 percent last fall -- blame it on "the federal government in general."

Vander Jagt said the survey results shows that "for the first time since the 1930s, the Republican label is not baggage" for GOP candidates. An open-ended question showed more volunteered positive comments than negative comments about the Republican Party, and the reverse was true for the Democratic Party . In 1974, by contrast, Republicans drew far more negative comments than did the Democrats.

On major issues, the Republicans have seized or widened a lead over the Democrats since the comparable survey last fall. On controlling inflation, their lead has increased from 8 points to 29. On controlling government spending, the gain has been from 17 points to 33. On holding down taxes, Republicans have gone from a 7-point advantage to a 21-point one.

On two international issues, Democrats have also lost ground. Republicans have gone from a 4-point deficit to a 1-point lead on maintaining world peace and from a 1-point lead to a 20-point lead on maintaining military security.

The most startling change has come on the traditional Democratic issue of unemployment -- now second in importance only to inflation. Last October, before the recession hit, Democrats had a 39-to-18 percent lead as the party most likely to reduce unemployment. In the June survey, Republicans had closed to a 41-to-38 deficit.

By a 3-to-1 ratio (32 percent to 11 percent) those interviewed said conditions in the country would be made better, not worse, by electing a Republican majority in Congress, while 51 percent said it would probably make no difference.

Among independent voters, there was a 5-to-1 majority favoring Republicans among those who thought the change would make a difference, though 54 percent thought a change in the controlling party would make no difference.

Vander Jagt said those margins held up even in districts with Democratic incumbents, but he cautioned that "we're not underestimating" the ability of those incumbents to survive an anti-Democratic trend by their own popularity and campaign efforts.

"The opportunity for massive gains is there," he said, "but whether we realize them depends on the job we do in the next few months. If the next four months are like the last six months, the sky is the limit."