Washington — Republicans should be smiling. The economy is improving. The President retains his personal hold on much of the public. William D. Ruckelshaus's appointment seems to have contained the crisis at EPA. And despite continuing problems at home and abroad, the President still seems firmly in command.
But Republicans - certainly GOP leaders - are troubled. They see a growing dissension within the party. Congressman Guy Vander Jagt of New York puts it this way: ''I think there is a serious danger of tearing ourselves apart from every direction.''
What Mr. Vander Jagt, chairman of the National GOP Congressional Committee, and other GOP leaders are talking about is what Vander Jagt pinpoints as, ''A growing, pent-up frustration among the more conservative elements of our party that perceive that Ronald Reagan has not carried out their agenda.''
The GOP right wing thought it had a top-priority commitment from Mr. Reagan during the 1980 campaign to give his first and foremost attention to their goals. Among those goals were the restoration of prayer in the schools, anti-abortion legislation, tax credits for private and parochial schools, and anti-busing legislation.
But the growing feeling among those on the party's right is that the President did not give what they called their ''social programs'' the attention he had promised - and that today his push for some of these objectives is not much more than token.
Many GOP conservatives are charging that the President has, in effect, been ''captured'' by more-moderate elements in the party. And they point to Vice-President George Bush and chief of staff James A. Baker III as leaders of what they see as a group close to the President who have moved him away from conservative commitments.
And these same conservatives are less than enchanted with the appointment of Mr. Ruckelshaus as the replacement at the Environmental Protection Agency. They remember his refusal as deputy attorney general to obey President Nixon's order to fire special Watergate investigator Archibald Cox. Some conclude that the EPA will be ruled by a very independent public official who is likely to please environmentalists at the expense of the business community.
Thus it is that Reagan is receiving as much, if not more, criticism from his own party's far right than he is from the Democrats.
At the same time - oddly enough - Republican leaders are becoming convinced that the President is the only Republican who could survive this intraparty dissension and win in 1984.
''The President has a tremendous personal capacity for healing rifts,'' said Vander Jagt at a breakfast with reporters. ''That's what he did in 1980. I'm not sure that I can see anyone else who could do that same thing in 1984.''
So Republican chieftains postulate that Reagan could, as he did in 1980, bring the progressives, moderates, and conservatives of his party behind him for another victory. Otherwise they see the clear possibility of a party split that would almost guarantee defeat for any other Republican candidate.
''I think Reagan will run again,'' said Vander Jagt. ''And I do think the Republican Party might tear itself apart if he doesn't run again.''
Asked why he thought Reagan would seek reelection, Vander Jagt said:
''I believe that he deeply feels that after the assassination attempt, these additional months and years are sort of a gift from the heavens and really not his to use as he sees fit.
''And I think he will agree with me that he, and only he, can hold the Republican Party together and thereby continue the new direction that he has started. And he will conclude that he has to run again.''