President Carter's relatively mild "windfall profits" tax proposal may end up being stiffened by the House Ways and Means Committee.

Interviews with key members show that sentiment is building among the panel's Democrats to increase the tax bite on the oil industry beyond what Carter has suggested.

Some committee sources say there is a better than even chance that the panel will vote to stiffen the White House plan. If not, they say, the committee almost certainly will allow vote on the issue when the bill reaches the House floor.

The new momentum in the committee appears to come from two camps:

A belief, primarily by liberals, that Carter's proposal is not tough enough and ought to be strengthened. The president's plan would make the oil compainies pay from $1 billion to $1.7 billion more in federal taxes each year than they might otherwise owe.

A conviction by senior members that some toughening is necessary for tactical reasons. Their reasoning is that, with the Senate likely to weaken the proposal, the House must start out stronger if the Carter plan is to pass Congress intact.

The new momentum could have a major impact on the legislation when the Ways and Means Committee begins hearings on Carter's plan next week. Panel leaders say they expect quick approval of the bill in time to send it to the House floor by early June.

The Carter proposal has sparked a major political scrap between the president and his chief Democrat rival, Sen. Edward M. Kennedy (D-Mass.). Kennedy has complained that the tax is too mild, and has charged that Carter yielded to the oil industry.

There is no single proposal around which the forces are rallying. However, several key members have sounded out top White House aides on the issue. Carter has said he would favor a tougher tax.

Reps. William R. Cotter (D-Conn.), Raymond F. Lederer (D-Pa.) and James M. Shannon (D-Mass.) have introduced a measure that would boost the tax rate on the Carter proposal to 80 percent of the "windfall" after exemptions, up from Carter's 50 percent rate.

Another proposal, by Rep. William M. Brodhead (D-Mich.), would reduce the exemption Carter's proposal makes for oil discovered before 1972 - one of the majre reasons that the White House plan would raise so little revenue.

The notion of toughening Carter's proposal has broad backing among many of the panel's 24 Democrats. However, oil-state lawmakers are expected to oppose any such move, and few of the panel's 12 Republicans are considered likely to back it.

Rep. Al Ulman (D-Ore.), chairman of the committee, has predicted that the committee will pass Carter's plan intact, but is said to be receptive to the idea of toughening it. House Democratic leaders also would like to see it stiffened.

Rep. Ken Holland (D-S.C.), one of several panel members interviewed yesterday, said he would vote for toughening the tax as "tactical proposition." Holland said that, if the Senate is going to trim the tax, "we'd better start high here."