Agriculture Secretary Bob Bergland is sweating out the latest in environmental issues: whether a nuclear power plant can be built on the banks of a stream nominated to be one of the nation's official scenic rivers.

Bergland's problem is all the more difficult for two reasons. Powerful members of Congress, including Senate Energy Committee Chairman Henry M. Jackson (D-Wash.), are pressuring him to decide in favor of the proposed $2 billion Sedro Wooley power plant on the banks of Washington's Skagit River.

On the other side are a host of environmental groups, Indian leaders and the fact that the nomination of the Skagit for inclusion in the act was made by President Carter himself during his environmental message last year.

Approval for the Sedro Wooley site about 50 miles north of Seattle is being sought by the Puget Power Co. The land is under the jurisdiction of the U.S. Forest Service, an arm of the Agriculture Department.

Under section 7b of the Wild and Scenic Rivers Act, Bergland must sign off that the nuclear plant site is environmentally acceptable before the Nuclear Regulatory Commission grants initial construction permits. Bergland's staff recently prepared an in-house assessment of the site that urged rejection on the grounds it would cause environmental harm to the Skagit.

An additional embarrassment is that the entire 158.1-mile length of the river and its tributaries was first proposed for inclusion in the act by the Forest Service.

The nuclear plant is the first major construction project to be proposed along one of the rivers covered by the 1968 act. Congress has yet to vote on Carter's nomination of the Skagit as a wild and scenic river but the provisions of the act grant full coverage to any river for three years after it is nominated.

"We don't regard this as a nuclear battle," said Mark Reis, a spokesman for Friends of the Earth, one of the groups opposing the nuclear plant site. "This will be a precedent-setting decision that will determine the way rivers under the act in the future."

Earlier this week 23 environmental sportsmen's and Indian groups sent a petition opposing the site to the White House. The Indians claim the plant will interfere with their treaty fishing rights.

Agriculture Department sources said yesterday that a quiet but potent lobbying effort has been mounted for the plant site approval by the entire Washington state delegation and the Nuclear Regulatory Commission, which has reported no potential harm from the proposed plant. Spokesmen for Washington congressional delegation members denied yesterday knowing of any lobbying on the issue.

Behind the lobbying, the sources said, is a move to get Bergland to declare the plant harmful to the river as a whole but recomment that the last 15 miles of the proposed scenic waterway near the plant be dropped from the act.

The sources said the proposed compromise has apprently gained favor with Bergland. "A lot of those involved don't like it but it's getting hard to stand up for our position and still satisfy the outside pressures," said one agriculture official.

Environmental groups yesterday angrily charged that the issue was being lobbied behind the scenes between the agriculture secretary's office and pro-plant forces.

"The proper form to do battle on this issue is before Congress in the open, not behind the closed doors of the secretary's office," said John McComb, a Washington representative of the Sierra Club.

McComb and representatives of other environmental and Indian groups opposing the plant said they would fight any compromise that allowed development along any part of the Skagit.