Washington — There are beginning, but significant, signs that many Reagan supporters are losing patience with the President's economic program.
GOP political leaders, both here in Washington and around the country, are expressing concern that an erosion of confidence in Mr. Reagan may have a negative effect on the fall elections.
And within the top levels of the administration, people now are uttering, privately, their fears that the continuing unresponsiveness of the economy to Reagan initiatives may (a) make it extremely difficult for the President to put his further economic plans into place and (b) lead to defeats in the fall that will mean even more obstruction in Congress.
From the South, where many Democratic conservatives moved to Reagan's side in the 1980 election, there are clear indications of growing impatience with the President. Herby Branscum, Arkansas Democratic state chairman, puts it this way:
''I think people are just beginning to nerve up enough to express disfavor with the direction Reagan is taking the country. I've begun to detect this in just the last 10 days or so. Up to then people were willing to give him what he was asking -- some running room. But his ground is beginning to run out.'' He continues:
''These are mainly people who voted for Reagan. One reason they have been willing to go along with him is because they felt their necks were on the line, too. But this is ending.''
Clarke Reed, from Mississippi and vice-chairman of the Southern region for the Republican National Committee, says that ''yes, there's much apprehension. It's not so much what the President is doing. But it is high interest rates. And our agricultural economy is in a terrible state.''
In other parts of the United States the erosion of support from Reagan voters is also in evidence.
Says Wisconsin GOP state chairman Ody J. Fish: ''From the time of the State of the Union -- and the indication of the size of the deficit -- there has been some nervousness around here.'' Mr. Fish adds: ''But I don't detect any lack of will to see Reagan's program through at this stage. You know everyone has been talking about biting the bullet. But it is easier to talk about it than to do it.''
Massachusetts Republican national committeeman Gordon Nelson says: ''People are really hoping the Reagan economy will start to work soon because the media are really giving us a going over and we'll be really hurt in the fall elections if interest rates remain high and unemployment is still very high.''
From the West, too, where Reagan probably remains strongest in terms of sustained support, come reports of some loss of confidence in the President's ability to turn the economy around.
''It's that immense deficit more than anything else,'' a Republican leader who asked not to be identified said. ''People who voted for Reagan say to me, 'I can't understand how he will go along with that deficit.' ''
But, in general, the assessment emerging from across America is this: The President still remains personally popular even as his supporters' confidence in what he is doing is starting to waver.
''It's a strange situation,'' says Thomas Guilfoil, Missouri's Democratic state chairman. ''His programs are increasingly unpopular. But he is not yet paying any political price for it. There is a curious separation between the President's programs and his popularity. Like the Eisenhower years.''
Mrs. Obera Bergdall, Oklahoma's Democratic state chairman, emphasizes this same oddity: ''After doing our own polling,'' she says, ''we see Mr. Reagan still popular as a person. But we also find that people are beginning to doubt his political strategy -- on everything. They don't know whether anything he is doing will work.''
Michigan GOP state chairman Peter F. Secchia concedes there is ''some anxiety'' about the President being able to turn the economy around. At the same time Mr. Secchia stresses Reagan's continued popularity and his own personal conviction that he is ''on the right course.''
Secchia also says that ''the people I talk to say 'give him more time.' '' But the dominant messages coming from political leaders, both Democratic and Republican, is that Reagan's time appears to be running out.
Mr. Guilfoil says that ''if the economy continues to worsen, I don't believe he will go beyond the next fall election without beginning to pay the price for his programs. And when the reaction comes -- it will be as severe as we have ever seen.''
The lagging economy and pessimistic forecasts are biting deeply into public confidence of the President. Alabama Democratic national committeewoman Dorothy Carmichael says: ''People are losing their patience with Reagan. They are mainly concerned for the elderly and the middle classes and feel his programs are for business and the rich.''
Says Mr. Branscum of Arkansas: ''There has to be some relief for this recession within 90 days or we really will be in trouble. The farmers here are really hurting.''
Republican Reed of Mississippi, a power among Republican politicians for a long time now, says the President is somewhat to blame for the fall-off in public confidence now because of having raised expectations of a quick boost for the economy.
''I feel that time is running out for the President,'' he says. ''Much of this is because of the President's self-imposed deadline. He has almost said he would provide instant relief. He will be held to this. He might have been better off if he had said he would be trying something different and it would take a long time for it to take effect. But he didn't.''