The House Ways and Means Committee may not seem the place for gleaning insight about overhauling the tax system. By liberal standards, the panel hasn't always been in the forefront of the drive for "tax reform." What little has gotten through has been the result of painful fights.

But its hearings this month on President Carter's new tax package have provided a graphic demonstration of why "tax reform" - at least as proposed by the president - isn't likely to get anywhere in this or any other session. The reason is simple: Americans don't really want it.

For the past four weeks, the Ways and Means panel has spent much of its time hearing "public witnesses" on the Carter "reform" package. Some 400 persons have testified so far. The sessions will continue another week or two, and then the drafting of the bill will begin.

The witness list has included leading corporate executives and spokesmen for single taxpayers, as well as groups such as the National Association of Retail Grocers and the Association of Independent Corrugated Converters. And they all have an axe to grind.

The issue is different each day, but the message almost always is the same. Inevitably, the interest groups testifying warmly endorse the portions of Carter's tax package that would give them bigger tax breaks. But they oppose most of his revenue-raising revisions.

The parade began with panels of witnesses from big business. Expectedly, they thought Carter acted wisely in proposing a cut in the corporate tax rate. But they bemoaned his attempt to end a big tax subsidy for exporters that most economists have contended is unjustified.

Then came the others: The AFL-CIO opposed Carter's bid to limit deductions for medical expenses. Restaurant employes lambasted his plan to pare back writeoffs for business meals. Bankers opposed a provision that would limit some of their tax breaks.

At the same time, mayors and governors criticized his taxable bond option for municipal bonds; Wall Streeters blasted his plan to limit some writeoffs on capital gains, and organized baseball hit his proposal to end business deductions for sporting tickets.

Nor have the demands been confined to the measures in the president's package. Utilities asked the panel to revive a proposal Carter earlier scrapped that would eliminate the president double taxation of profits and dividends. And several other groups are seeking special relief.

By the time the hearings end next month, virtually none of the so-called "loophole-closing" measures Carter has proposed will have escaped opposition from some special interest groups. The few "tax reform" advocates supporting the Carter plan have little, if any, clout.

The daily line-up of special interest groups has proved somewhat discouraging for key Carter administration officials, some of whom - being new - haven't seen it all before. As a Treasury official sighed, in jest, last week: "It sure is nice to see everybody behind the program."

In a way, the flap may seem ironic. While Carter's tax package age can be criticized on technical grounds, it certainly isn't nearly as sweeping as the one he promised during the campaign or considered last September. If anything, the program before committee is sharply cut back.

But the ritual being acted out in the Ways and Means Committee does show the difficulty Carter, or anyone else, is likely to face in trying to push broad changes in the tax system through Congress. While people may say they want it, they really don't in the crunch.

A Brookings Institution study last September showed that a sweeping overhaul of the nation's tax system that eliminated most deductions would enable the government to slash tax rates dramatically - to a range of 10 to 44 percent from the current 14 to 70 percent.

The problem is, no one wants his own deductions to be among those to go, no matter how big a tax cut the government promises in return. Sensibly or not, Americans would rather keep the chance to claim loopholes of their own, even if it means tax rates must stay higher.

So it is that a Harris poll made public this week can report that "despite forecasts by key congressional leaders that President Carter's proposed tax program will have a hard time passing the House and Senate, it meets with a substantial 55.16 percent approval by the . . . people."

And a Roper Organization survey last summer showed that while Americans say they want more equity and lower taxes, they aren't willing to give up the tax deductions they claim now to help finance any major changes. If anything, more breaks and deductions may be on the way.

That is what the witnesses have been saying in the Ways and Means Committee over the past few weeks. That's what they'll say in coming weeks. And that's why most experts think it's unlikely that Carter will win more than a handful of the $9 billion he's proposed in tax "reforms."

It's a tiresome - and often frustrating - process to sit through Ways and Means hearings on tax legislation, even for a good many of the members. But it does provide some insights on why tax legislation succeeds or fails.