Tax bill sparks praise, criticism, and doubts. President Reagan will take primary credit for the historic tax-reform bill originally promoted by Democrats. So far there does not appear to be a public groundswell of enthusiasm for the measure, and it even seems to have lost the President respect from some in his party. Still, the bill should spread taxes more evenly.

President Reagan is poised to sign a comprehensive tax-overhaul bill that is bound to have a far-reaching economic and political impact. In political terms, the sweeping reform gives the Reagan presidency a needed lift. Although the Democrats were the first to promote tax revision, the President made it the centerpiece of his second-term economic agenda, vigorously pushing it in the public arena. He will take primary credit for the bipartisan achievement.

But both Republicans and Democrats will try to capitalize on reform in the fall elections. If the Democrats manage to capture control of the Senate, it is possible that Sen. Bill Bradley of New Jersey, the intellectual spark behind the reform, will be propelled into a Senate leadership role.

In economic terms, the removal of a confusing welter of tax deductions and shelters will force United States businesses and individuals to make financial decisions based on economic rationality and profitability rather than tax advantage.

The reform will also spread the tax burden more fairly: 6 million poor families will be removed from the tax rolls and many low-income families will have their tax liability reduced, while corporate business will pay more.

The public verdict on the Tax Reform Act of 1986 is out, however. And it will be out until April 15, 1988, when Americans will file their first tax returns based on the new code. So far there does not appear to be a groundswell of enthusiasm for the measure; there is in fact an undercurrent of unease.

``This was never a big issue in public opinion,'' says William Schneider of the American Enterprise Institute. ``Only a minority think they will pay less.''

If American voters do not find themselves getting a benefit from the changes, and they will be filing their returns just when the US political primaries are under way, tax reform could backfire, and both Republicans and Demcocrats risk being hurt.

``The problem is whether this will be regarded as something good and great or as something abysmal and stupid,'' comments political analyst Horace Busby. ``Something akin to a taxpayer revolt could be a negative thing politically . . . but that's in the future.''

Mr. Busby notes that reform appears to have lost Reagan a certain amount of respect among Republicans, who feel that what was passed was essentially an anti-Republican bill and that the President never looked at the fine print. Some Senate Republicans, notably Sen. John Danforth of Missouri, strongly criticize the reform, charging that it will burden business, further erode the industrial base, and lower standards of living.

But the Senate passed the tax act by a robust margin of 74 to 23. Forty-one Republicans and 33 Democrats voted for the bill; only 11 Republicans and 12 Democrats voted against it.

For the moment Reagan administration officials are sounding the trumpet of victory. ``This will benefit the economy,'' said Treasury Secretary James A. Baker III Sunday, emphatically rejecting predictions of dire consequences.

For their part, many economists applaud the tax overhaul, while recognizing that a 925-page bill is far from ``simple'' for most taxpayers and that it retains a plethora of benefits for isolated businesses and wealthy individuals.

On balance, supporters say, the bill will mean greater fairness and rationality over the long term.

``This will induce business to marshall its resources in a far more efficient way,'' says conservative Alan Greenspan, a former chairman of the President's Council of Economic Advisers.

But there are also concerns. One is that it may now be harder politically to raise revenue to deal with the persisting problem of a budget deficit approaching $230 billion. Few politicians, Democratic or Republican, think the deficit can be licked without a tax increase, but their constituents, waiting to see how tax reform will work out in practice, may not warm to such talk. This could worsen the deficit problem.

Another worry is that failure to index some items, such as depreciation and capital gains, could cause distortions and unfairness if the US economy experiences another period of inflation.

Discussion of the reform focuses largely on its impact in the transition years, when individuals and businesses will be in the throes of changing their decisions and plans.

Overall, the tax bill is expected to pull in $11 billion more in 1987, then result in lower revenue in the following two or three years, and finally end up being ``revenue neutral.''

In the view of some experts, these swings will not have a significant impact. ``Given a $4.5 trillion economy, any minor ripples that might be caused are not going to have an appreciable effect on the economy,'' says John Palmer of the Urban Institute. ``And in the longer run there will be efficiency effects.''