As some Democrats in the House see it, the first months of the Carter administration have been a learning experience for both the new President and the new Democratic congressional leadership.

President Carter is learning, as House Democratic Whip John Brademas (Ind.) puts it, that House Speaker Thomas P. (Tip) O'Neil Jr. (D-Mass.) and Senate Majority Leader Robert C. Byrd (D-W.Va.) "are not employees of the White House."

And the Democratic leaders in their turn are discovering that individual members are not employees, either, but highly independent legislators who frequently are unimpressed by party-line appeals.

The nature of this independence was brought home painfully last week to the administration and the congressional leadership by delay of two Carter-backed bills that were supposed to sail through the House.

The first of these bills was the measure to relax the Hatch Act and allow federal employees to participate more fully in politics. It was withdrawn after passage of an anti-union amendment prohibiting the expenditures of union dues for political purposes.

What surprised the Democratic leadership was that 94 Democrats voted for the amendment, which was offered by Rep. John Ashbrook of Ohio, a highly conservative Republican.

"In the old days it would have been enough to say that Ashbrook was for the amendment and labor against it," said a leading Democrat after the late-night vote. "But that approach doesn't work anymore."

Nor did the partisan approach work on a bill considered certain to benefit Democrats, the President's election-day registration proposal. A preliminary whip count taken by the leadership showed that several Democrats who had been presumed to favor the bill were undecided about it.

The bill was promptly pulled off the House schedule and delayed until late June to allow the administration time to do some lobbying.

What is happening in the House is seen by some as a harbinger of eventual confrontation between Carter and the Congress or as a diminution of the traditional strength held by organized labor on the Democratic side of the aisle. But other Democrats see the unresolved problems and the delays as an indication that reforms of congressional processes are working beyond their wildest expectations.

The House is now in many respects the "open institution" that the reformers of a few years ago wanted to make it. Committees operate with a high degree of independence, the younger members are allowed to talk as well as be seen, and amendments even from the minority are frequently considered on their substantive merits.

"In my opinion, the big change has come in the caliber of the members," says Gary Hymel, the administrative assistant to Speaker O'Neil. "In the old days the congressmen followed the reports of the committee and voted the way the committee wanted them to vote. Now the members are young, bright, highly educated, independent.The voters are more educated, too, and the press does a better job of telling them what their congressmen are doing. It makes it infinitely harder for the leadership."

Fifty-three per cent of the House members on the Democratic side are new in the past two terms. Many of them have no intention of approving legislation merely because it carries a presidential stamp or the imprimatur of the leadership.

"There's not going to be an automatic response to legislation unless it's well thought out," said Rep. Norman Y. Mineta (D-Calif.), a former San Jose mayor elected to the House in 1974. "The way the Hatch Act bill was handled was a shame, a debacle.It was just badly managed, and some of the members were protesting that."

The protests against this "bad management" sound remarkably similar to the complaints that a number of Democratic leaders have about the Carter administration - namely, that some of its members don't do their homework or know what is going on.

Carter has acknowledged that this criticism sometimes has been valid.

"I've had a lot to learn in these first three or four months in office," the President told a group of Northeast congressmen last week. "I've had some good instructors - many of you right in this room.

But a lot more instruction may be needed, in the view of some on Capitol Hill.

"The whole administration is having trouble communicating easily with the Congress," said Alice M. Rivlin, director of the Congressional Budget Office. She believes there has to be "much more communication" than once was necessary with Congress.

It is not surprising that Carter came into office without realizing this. The only experience he had to guide him was the Georgia legislature, and that wasn't much of a guide.

In Carter'r four years as governor he was faced by a vocal opposition led by Lt. Gov. Lester Maddox, who under Georgia law was leader of the legislator. The mutual distaste Carter and Maddox felt for each other translated itself into legislative relationships and sometimes dominated them.

Even so, there are those close to Carter who think that he has fundamental problems in relating to legislative bodies. James David Barber, in dealing with the Georgia legislature, "The Presidential Character," quotes Carter's top aide, Hamilton Jordan, as saying that Carter "doesn't understand the personal element in politics."

Barber says that Carter was "late to compromise, hard to convince" in dealing with the Georgia legislature, but observers that he eventually got his reorganization plan recently when he answered a question from a Harvard student who was critical of Carter's relationship with Congress.

"Jimmy Carter is an executive rather than a legislative personality." Watson said.

While he defended most of what Carter had done to date, Watson acknowledged some validity in the criticism by saying, "We must understand that Congress has a very legitimate role to play."

So far, that "legitimate role" has yielded a reasonable number of successes, including the public works and economic stimulus bills. Carter's reorganization proposal for a department of energy is moving swiftly through the Congress.

After the President reviewed administration proposals with Democratic leaders last week, he said it was "amazing how many of these have already been passed by the Congress or are well on the way to passing."

But there have been failures, too, especially last week, and there are tough challenges ahead on the Clean Air Act, the legislation to create a new consumer protection agency and the President's energy package.

House Majority Leader Jim Wright (D-Tex.) said at a news conference Friday that he knows Congress "didn't perform too courageously two years ago" in failing to pass energy legislation. He said it is the leadership's job "to get enough starch in the spine" to do better this time.

Wright called the energy legislation "the greatest challenge to the Congress" and predicted that the House would complete action by the end of July.

What that action will be is uncertain. Some House members are genuinely opposed to the gasoline tax. Others are worried about constituent reaction. Still others are concerned that Carter will go over their heads again and make a direct appeal to the people.

"This television, town-meeting stuff is very worrisome to some of the members from marginal districts," said one veteran Democratic congressman last week. "Nixon and Ford both ran against Congress and now it seems that Carter is doing the same thing."

Brademas feels that the conflict is exaggerated by the press.

"The media seems to feel like Carter and the Congress are two gunfighters who are going to have a shootout at high noon and leave one or the other bleeding in the dust," he said. "But that isn't the way the political systems works. We fight on Tuesday and compromise on Wednesday."

The problems of the Democratic leadership have been compounded by newfound cohesion of the Republicans. The Democrats have big, unwieldy majorities in both houses and the GOP forms alliances with different wings of the majority, depending on the nature of the legislation.

These alliances take advantage of the regional conflicts within the Democratic Party. On common site picketing, the successful coalition that defeated the bill included Republicans and Democrats from anti-union areas of the Sun Belt. This week, on the Clean Air Act, Republicans are likely to find themselves allied with Democrats from auto-producing constituencies in the East and the Midwest.

But it is the independence of Democratic members rather than the cohesion of Republicans that has, in the early months of 1977, made life most difficult for the leadership. And if the congressional reformers of past years can be believed, this is as it should be.

"The new members are very selective," says Mineta. "A number of us feel that we don't have to go along with the New Deal approach of throwing money at a problem, hoping it will go away. We want to target our resources . . . In the long run that means we're going to be with Carter more than against him. We're his natural constituency."