Two new polls show the Republican Party gaining ground on the Democrats in public support and the handling of most key issues, and moving into a position to challenge seriously for control of the House of Representatives in 1982.

A June survey taken for the Republican Congressional Campaign Committee by Market Opinion Research Corp. of Detroit showed the GOP a shade ahead of the Democrats, 51 to 49 percent, in a mock congressional election.

A Gallup Poll taken about the same time showed the Republicans trailing, 49 to 45 percent. But both polls showed a clear trend in favor of the GOP in all three basic measures -- party identification, issue preference and voting intention.

Rep. Guy Vander Jagt of Michigan, chairman of the Republican Congressional Campaign Committee, said his own poll "confirms our belief that 1982 is the year for Republican control of the House."

George Gallup said his company's figures suggest that the traditional midterm election losses for the party in control of the White House "could be somewhat blunted if present GOP gains are sustained. At the same time, however, the findings provide little basis for believing that the Democratic Party will lose control of the House in next year's congressional elections." p

"I look at four special elections and we beat'em in one they've contolled for nine years and one we came within 300 votes in a district they'd held for 45 years," says Rep. Tony Coelho of California, chairman of the Democratic Congressional Campaign Committee. "That's where the real polling takes place. They may want to ask their candidates in Ohio and Mississippi what the people are really thinking."

A switch of 27 House seats would be necessary for the Republicans to gain a majority in the House.

In the view of political observers, the pro-Republican trend line measured in both polls six months into the Reagan administration is more significant than the relatively minor differences in the absolute numbers.

Both polls showed the gains were particularly noticeable in the South and the West, among younger voters and among Catholics.

Robert Teeter, president of Market Opinion, said the gains were attributable to President Reagan's personal popularity, strong public support for his economic policies and the GOP's improving image as a party.

Teeter's figures showed that in basic party identification, the Democratic advantage has shrunk from 16 points last June to 7 points in the most recent survey. Counting in independents who lean to one party or the other, the Republicans have cut their deficit from 16 points down to 1 point.

The Gallup figures, which exclude the independent leaners, show the GOP deficit shrinking from 24 points to 14 points.

Both polls showed economic issues far more important to the voters and both said the Republicans have erased the Democrats' long advantage as the party of prosperity. Gallup gave the GOP a 13-point lead in that regard, the first such advantage in three decades.

Teeter said Republicans now enjoy a 51-point lead on controlling government spending, a 46-point lead on balancing the budget, a 45-point lead on controlling inflation and a 38-point lead on holding down taxes. In his figures, the Republicans have edged ahead of the Democrats by 1 point on reducing unemployment -- the first time he has shown them ahead in that regard.

Teeter flagged two potential trouble spots for the Republicans. His poll showed the Democrats have a 43-point edge as the better party for helping the elderly -- a reflection, he said, of public reaction against Reagan's propoed Social Security cuts. A separate question of Teeter's found that two-thirds of those polled said Social Security benefits should not be reduced in any way.

Teeter said, "Republicans have to be cautious about the Social Security issue," and that "a big debate on the social issues [abortion, school prayer, homsexuality] would be a great mistake." Such issues are less important and more divisive than the economic issues, Teeter said, and "to the extent the social issues take away from the economic issues, they hurt the [Republican] party."

Teeter's poll was made public as the Republicans began their first campaign school for potential 1982 House candidates. Officials said the 89 who registered was the largest contingent of candidates ever to attend such a session so far in advance of the election.