The Interior Department's Fish and Wildlife Service, swallowing hard, has mailed to its field offices about 11,000 packets of educational material on bald eagles that it bought from the National Wildlife Federation.

The federation is not in the best of graces at the department, considering its outspoken criticism of Interior Secretary James G. Watt. The packets were ordered last August and delivered in December, but it wasn't until late last month that Deputy Director F. Eugene Hester discovered the bill for them in a routine review of extension service activities.

At that point, as they say, the feathers hit the fan.

Department officials, mindful of Watt's directive to review all "subsidies to special-interest groups," were concerned that the packets were part of a federation membership drive, a matter of some sensitivity at Interior.

As Alan Levitt, a Fish and Wildlife spokesman, noted, "These people have campaigned against the secretary."

The packets are directed at schoolchildren and their teachers, and consist mostly of pictures and facts about the American bald eagle. This year marks the bald eagle's 200th anniversary as America's symbol, and the federation has chosen the bird as the theme of its annual wildlife week celebrations March 14-20.

The federation's name is prominent on many of the materials, and the phrase "Join and support the National Wildlife Federation and state affiliates" is lettered across the bottom of two large color posters in the packets.

Federation officials say its packets have been sent out by the Fish and Wildlife Service in years past, but Levitt said this is the first year the federation has charged the government for the packets, at a time when agencies throughout the government are taking a sharp pencil to subscription and publication budgets.

The material cost Fish and Wildlife $2,500, and while Levitt concedes that the agency couldn't have produced comparable material for anything close to that price, he says it is "very unusual for us to purchase outside publications, especially under the current budget climate."

But the agency was also sensitive to the public relations aspects of refusing, at this late stage, to send out the packets. Many Fish and Wildlife field offices sponsor activities for wildlife week, which has been promoted by the wildlife federation since Franklin D. Roosevelt proclaimed the first one in 1938.

Not only that, but President Reagan recently lent his support to celebrations on behalf of the bald eagle, proclaiming 1982 the "Year of the Eagle."

So, about a week after Hester put a hold on them, the packets were approved for distribution.

Levitt insists the delay was not, as federation officials suspect, part of a vendetta against the federation. "We're simply very sensitive to the use of funds," he said. "We don't want to contribute to or support these organizations."

But he said he is seeking contributions of informational material from the corporate world as a way of augmenting his dwindling publications budget. The agency already has on hand 50,000 copies of a bald eagle brochure from another outside source: Seagram's, makers of Eagle Rare Bourbon