Many Republican leaders in Washington and around the country are calling for substantial reductions in the massive budget deficit - even if it means cutting defense spending.
These leaders insist that the United States must keep a stout defense. Some say better defense management is the chief way to achieve savings.
But a growing number of these Reagan supporters want the President to make certain that America's defense capability doesn't exceed its need. They are asking Mr. Reagan to take a hard look at the highly expensive weapons systems in his program to see if some can be pared or eliminated.
One Midwestern GOP state chairman says, ''I talk to a lot of people and a lot of politicians. There now is widespread support for reducing defense spending - or at least holding down increased defense spending.''
In Maryland, state Republican chairman Allan Levey says, ''I think there will be some cuts in defense. We need a strong defense -- but I think there will be some cuts.''
Fred Cooper, Georgia's GOP chairman, says, ''Most people are appalled at spending so much money on defense. I'm for some cuts in the defense budget - but not dramatic cuts.''
In New York, a large number of county chairmen now say they want the President to compromise on defense spending. And at recent GOP county conventions in Iowa, a number of the platforms advocated holding down defense spending.
From the far West comes this judgment from a GOP political leader: ''The President simply cannot ignore cutting defense. There's a lot of fat there.''
There also seems to be a growing feeling among Republicans on Capitol Hill - often expressed privately - that the President can't provide meaningful budget reductions without making substantial cuts in projected defense spending.
At the same time, Republican leaders report evidence that the President in recent weeks has been able to shore up flagging support.
They attribute this to Mr. Reagan's trips around the US, where he has taken credit for reduced inflation and some lessening of interest rates. GOP leaders also say the change has resulted from Reagan's criticism of the press. The nation's chief executive has lashed out at the media for holding him responsible for a recession which, he says, had its roots in previous administrations. He contends that his economic program is only now being adopted - and only in part.
GOP leaders say the public, which is generally unhappy with the press, was quick to take Reagan's side when he charged the media with unfairness.
Many GOP leaders express their displeasure with press treatment of Reagan. Says Martha Bell Schoeninger, Pennsylvania state chairman, ''He is getting a lot of adverse propaganda from the press -- and it doesn't help a bit.''
In early March, a Monitor survey of GOP leaders found many expressing concern over what they saw as an erosion of confidence in the President's economic program. Now their view is slightly more rosy.
Mr. Cooper says polls in Georgia ''show people want to give the President more time to put his program over. People are not happy with the economy -- but they are giving the President more time.''
Florida Republican chairman Henry B. Sayler says he now is convinced that Reagan should be given at least a year, perhaps two years, to show that he had the answers for the economy.
''The President is doing pretty well,'' he says. ''Not as well as the first year. But nobody would expect he would. He has a lot of ardent admirers in this state, Democrats as well as Republicans. People still think his program is right -- and that he should stick with it.''
Minnesota state GOP chairman William Morris says a new poll of voters in his state ''shows Reagan's popularity very strong - just about the same as it was in the middle of last year.''
Mr. Morris says this poll also asked: ''How long do you feel we should give Reaganomics to work?'' Forty-six percent gave Reagan ''one year more''; 32 percent ''six months to one year''; 10 percent say his programs ''should have worked by now''; and the remainder, ''do not know.''
In Illinois, GOP state chairman Don Adams cites a recent poll ''showing Reagan with a very strong popularity rating, 67 percent. This was only 1 percentage point down from a poll we took six months ago.''
Even in Michigan, with the highest unemployment rate in the country, GOP state chairman Melvin L. Larsen says, ''The majority of the people I talk to remain patient with what the President is doing to try to bring interest rates and unemployment down.''
Robert O. Voy, Oregon state chairman, says that ''our economy is down, unemployment over 11 percent.'' But he adds, ''I don't get the impression that there is any relationship between this and attitudes toward the President.''
Many of these leaders, who a few weeks back were concerned that they were rapidly losing public support, now seem less pessimistic. They still express concern over GOP election prospects if the recession lasts into the fall.
Says Mrs. Schoeninger, ''He (Reagan) must do something by summer about the economy. It is important to all of us. To elections and everything else. But I'm an optimist. I think things will be better by summer.''
Tim Hyde, executive director of Iowa's Republican state committee, says, ''Yes, I do see a falloff in public confidence in the President, among Republicans and voters generally. It is hard to measure how severe it is. It is not a repudiation of the President, nor a wish to abandon the course he is on. This is good news for the President. He has time. But not for us. We have a special election for the legislature and fall elections coming up.''
Gordon K. Durnil, Indiana state chairman, says, ''I think Reagan is holding strong. But the 13.6 (percent Indiana) unemployment rate must get better before the fall elections. The voters' perception must be that unemployment is going down.''
Andrew S. Natsios, Massachusetts GOP chairman, comments, ''If by the fall, late August, or early September there are not some signs of improvement in the economy, we may have some difficulties at the congressional level. But not in state races -- corruption is one of the big issues there.''
Mr. Natsios adds, ''There have been a couple of dozen Democratic members of the Massachusetts Legislature who told me they voted for Reagan -- and who still say they are sticking with Reagan.''
The general view from GOP leaders, that the public feels the President's economic program will eventually succeed, is in line with a new New York Times-CBS poll. The survey shows that 54 percent of the American people are convinced this program will finally have a positive effect on the economy. Still , this number is down from 60 percent two months ago.