When President Carter sent Congress his tax-cut proposal last January, most people expected the bulk of it to survive intact. By last week, however, it seemed that after months of delays and abortive rescue efforts, Carter finally had lost control of the measure. There even were some suggestions that there may be no tax cut at all.

The turning point came Tuesday, when the House Ways and Means Committee announced that, despite threats of a presidential veto, it would start work this week on a "compromise" tax bill containing a cut in capital gains taxes. Barring a committee turnabout on a last-ditch counterproposal the administration is preparing, it now seems likely the compromise will pass.

Moreover, unless Carter's influence grows dramatically in the next few weeks, the White House may be powerless to affect the tax package either on the House floor or in the Senate. Besides the prospect that Ways and Means will include the capital gains tax cut in whatever measure it approves, the administration also faces these possibilities:

A serious tactical challenge from the GOP-sponsored Roth-Kemp taxcut bill, which previously had been discounted by Democrats. The proposal, designed to slash taxes by $100 billion over three years, is regarded as unrealistic by many economists. But it has gained popular appeal in recent weeks. White House officials already are scrambling to counter the move.

The possibility of a floor stampede for costly new tax breaks for small business. The Ways and Means compromise contains a graduated income tax for the first $100,000 of business income, but House leaders fear a floor try for a second proposal by Rep. Neal Smith (D-Iowa) that would raise that to $300,000 and add new tax breaks. Members also might widen the capital gains tax cut.

Even if the bill makes it through the House promptly, it faces more serious tinkering in the Senate. Majorities in both the Finance Committee and the full Senate already have endorsed a sharper cut in capital gains taxes than the House is likely to pass, and both bodies are almost certain to tack on a slew of special-interest tax breaks.

If Carter does veto the tax bill, it's nowhere near certain that Congress will pass a "cleaner" tax cut - even if the lawmakers are called back for a post-election session, as some administration strategists now envision, congressional sources say the law-makers could go either way - send the same bill back to Carter again, or scrap the tax cut entirely.

Indeed, a good many House and Senate members now appear convinced it wouldn't really matter if the tax cut fell through. The Congressional Budget Office estimated this month that failure to enact a tax cut would result in only a scant rise in the unemployment rate. Without the threat of massive new joblessness, a veto could backfire.

How did Carter get into such a mess?

The answer involves several factors: A growing conservative mood in the country that has made voters suspicious of the kind of tax cuts Carter has proposed; ineptness and refusal to compromise on the part of some White House advisers; and ineffectual leadership in Congress. The result is, chaos now prevails.

The package Carter proposed in January was a traditional Democratic tax-cut plan with a few populist extras. Congressional leaders warned Carter's proposed "reforms" might pose a problem, but there was agreement back then that a tax cut was needed to help the economy. The major question was whether Carter's bill would to help the economy. The major question was whether Carter's bill would provide enough relief to offset the impact of inflation.

But before the measure got to Ways and Means, the mood of the country changed visibly: Upper-middle-income taxpayers, hit hardest by this year's rise in Social Security taxes, grew wary of Carter's plan. A new burst of inflation sent voters worrying about the budget deficit. And opposition to the tax "reform" proposals mounted.

By the time Ways and Means seriously started working on the bill, it no longer was a question merely of "saving" Carter's reform package. The problem had become how to stem the congressional push for a spate of conservative proposals aimed at relieving upper-middle-income taxpayers. The House already has passed a tuition tax credit bill that Carter opposed. And more is on the way.

What has stood out visibly in the foray is the ineptness of the administration's own lobbying effort. Carter seemed at first not to believe that the tax bill was in trouble, and reluctant - once he realized the problem - to do much to try to rescue it. (His recent press-conference tirade against the capital gains cut, for example, did more to help that measure than to hurt it.)

The Treasury's Hill operations were somewhat less bumbling, but Treasury Secretary W. Michael Blumenthal, who got into the act late himself, has been prevented by Carter's White House lieutenants from compromising much with the lawmakers. Too often, the the administration's strategy has been simply to wait until Congress seizes the initiative.And by then the battle is lost.

Perhaps the most eye-popping performance, however, has been by the Ways and Means Committee. Although usually not a very partisan group anyway, Democrats on the panel have been splintered this year beyond the usual liberal-conservative split, with some onetime "tax reform" advocates backing a rollback of existing reforms - or threatening to scuttle the bill altogether.

Moreover, Rep. Al Ullman (D-Ore.), the committee's chairman, has seemed virtually unable to exert any influence on the panel. When the committee bogged down last April over Carter's reform proposals, Ullman cleverly called a recess to give panel members time to cool off. But critics say he hasn't used the hiatus to any advantage. If anything, Republicans have gained from the recess.

Ullman's handling of other tax issues also has raised some eyebrows. On the capital gains issue, Ullman turned to a relatively junior member, Rep. James R. Jones (D-Okla.), to put together a compromise as a replacement for a more stringent cut proposed by Rep. William A. Steiger (R-Wis.), and then endorsed the measure as the "Jones-Ullman bill" when it appeared likely to be the panel's major vehicle.

Some disgruntled liberals joke that Ullman would "provide the 19th (majority) vote for anything that flies."

Nor have top House Democratic leaders done much to help the president push his package through. Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who was active in getting the energy bill started through Congress, has let the Republicans make hay out of the Roth-Kemp and capital gains issues without so much as a whimper. And Majority Leader Jim Wright (D-Tex.) barely has kept track of the issue.

The result is that control of the committee - and the tax bill - has gone by default to the panel's 12 Republicans, who are backing their own proposals and have no urge to see Carter succeed. In large part because of GOP influence, Carter now is facing the prospect that the panel will enact the capital gains cut, which effectively would repeal the "minimum tax" that reformers won in 1969.

(Capital gains are the profits from the sale of stocks or other assets. Only half a capital gain is subject to the regular income tax, but the remainer is liable to the minimum tax if first over $20,000.)

If Carter vetoes the overall legislation, there's no telling what Congress would do - from simply overriding the president's action to scrapping the tax measure entirely. (The betting these days is that the president won't reject the congressional measure. Ullman said last week the thought the Jones compromise would "look good to" Carter after he saw what the Senate would do.)