The pummeling that President Reagan took at the just-completed meeting of the nation's governors here was -- in the eyes of governors of both parties and of many administration officials, as well -- an unnecessary drubbing. It says something fairly serious about the problems the president still has in being master of his own house.

To boil down a complicated story to its essentials, the administration was unable to produce, in six months of trying, a coherent program to fulfill a pledge that Ronald Reagan himself had designated as the centerpiece of his 1982 domestic program.

When the president introduced his federalism initiative in the State of the Union address, he described it as a "bold stroke" to turn over to the states the authority to manage dozens of domestic programs that have been run in Washington. He was candid in saying that the details had not been fully developed -- and would not be until administration officials had consulted fully with governors, state legislators and county and city officials.

The discussions began during the regular mid- winter meetings of the state and local officials, with the president setting the target of having the program ready for submission to Congress by April 1. The timetable slipped, as timetables have a habit of doing. But there was a deadline, imposed by the cycle of summer meetings of the various negotiating groups. By June 1, the positions of all the state and local groups had been well defined and the differences with the original Reagan position had been significantly narrowed. What remained was for the president and his principal advisers to resolve their own position on the outstanding issues.

The White House never did that. The reasons (so far as I can learn from governors and legislators of both parties and from administration officials) are disquieting. For one thing, those who control the president's schedule were apparently unwilling to add this topic to an already bulging agenda. In a real sense, the battle of Beirut knocked out the federalism initiative.

But there was more to it than that. In every account, from every source, it is clear that some senior officials were using the president's distractedness to delay a project that they all along wanted to kill or subvert. At the meeting here, a couple of the culprits were named publicly: David A. Stockman, the budget director, and Robert B. Carleson, special assistant to the president for policy development.

Instead of being out front on an issue he had made his own, Reagan is now seen as foot-dragging. Last Friday, he had to make personal phone calls to key governors and legislators to apologize for the situation and to promise his renewed attention to the issue next year. It was, at least, an embarrassment.

Some of those involved, insiders as well as outsiders, say it reflects the dangers of a staff system with several roughly coequal heads -- Jim Baker, Ed Meese, Bill Clark, Mike Deaver and Stockman -- and several others who have carved out running room in the gaps among those principals.

One would like to think this is a unique example of the breakdown of the system. But the odds are heavily against it. That means the president has a problem on his hands -- a problem only he can solve.