Washington — There is growing anxiety among Republican leaders that the lagging budget-making process is causing the Reagan administration to drift.
While allegiance to the President still holds firm, GOP chieftains in all geographical regions now are beginning to raise these questions:
* If the budget stalemate continues for much longer, will it be possible for President Reagan to regain his momentum?
* Won't a protracted impasse over the budget look worse for the President than for Congress - simply because it is natural for the American people to expect their chief executive, not the legislative branch, to provide the initiative to keep the government moving?
Again and again GOP state leaders told the Monitor, in a nationwide phone check into their current views, that the people in their regions were growing frustrated over the bogged-down economy and the budget.
At the same time they said that patience with the President still held.
''The informed electorate and party leaders feel we must get a settlement on the budget and go forward,'' says Iowa's state GOP chairman, Bennett A. Webster. ''The interest rates are killing us. And to get interest rates down, we are told , we must reduce the deficit.''
Says Dennis M. Olsen, Idaho's Republican state chairman: ''There is no question but what people here, by and large, feel the issue should be resolved - so they will know what to expect with respect to taxes. The feeling here is that the President should not abort his plan, that it hasn't had time yet to take effect. But the impasse should be broken so people know how to plan and what to expect.''
In Washington, presidential domestic policy adviser Edwin Harper told a group of reporters over breakfast that there was ''tremendous pressure (from the business community, political leaders, and the public) to put our fiscal house in order.''
''The first step,'' he said, ''is a credible cooperation on the budget.''
Mr. Harper underscored Mr. Reagan's desire to put the budget process behind him and ''get on with the nation's business.''
Meanwhile, even as Sen. Bob Dole (R) of Kansas insisted that a budget resolution might be within reach, White House and congressional budget negotiations seemed to shelve the idea of working for what the parties would call a full, substantive compromise. Instead, they now seem to be focusing on an approach that would merely cite budget goals and let Congress hammer out the details.
Such a resolution, some observers here say, would do little to relieve the conflict between the President and Congress on such issues as defense and tax cuts. Thus, the deadlock might well persist.
Democratic leaders, too, report growing public frustration over the unresolved budget. But as might be anticipated, they uniformly say the people they talk to are putting most of the blame for this on the President, not congressional Democrats.
''There is a perception that we all wish all things were in better control,'' is the way Don Adams, GOP state chairman for Illinois, puts it. ''But there is still a margin of patience with Reagan. Everyone wishes the budget would get resolved.''
There were a few GOP leaders, particularly in the South and Southwest, who say they don't see this concern over the budget. Says Perry Peters, executive director of the Republican Party in Arizona: ''I'm sure we are not typical here. We have a lot of die-hard Reagan supporters. Among party people I talk to there doesn't seem to be real concern about delay.''
''Among the people at large, I have found some impatience over high interest rates - and some feeling that if the budget is cut, interest rates would go down.''
Delaware's Republican chairman, Jerome O. Herlihy, says: ''The people I talk to are increasingly concerned with the stagnation of the economy. There is a feeling that the President wasn't responsible for getting into this recession - but now it is time for him to get us out of it. Yes, he has some responsibility to get us out of it.''
In New Jersey, Frank Holman, state Republican executive director, says, ''People believe that it is time to get the budget enacted and get on with the nation's business.''
''They ought to get on with it,'' says -Arkansas' new state GOP chairman, Robert Cohee, of the budget process. ''Interest rates must be reduced. And that of itself would probably cause unemployment not to be so high. And that would increase the revenue. . . . I think the President has made his position clear. Now it is up to O'Neill to come up with his program.''
Says Greg Beuerman, executive director for the Republican Party in Louisiana: ''There is a lot of talk about the budget deadlock. If it goes on much longer, everyone will be impatient. There is a feeling it is time to get on with the nation's business. We are reaching time for decision -- a compromise if that is what has to be. But people I talk to desire that the President's position be dominant in such a compromise.''