When the proposal for a new college tuition tax credit began gathering momentum in Congress last autumn, it seemed a classic example of how good intentions often can make bad tax law.

Although many upper-middle-income families hailed the tax plan, there was broad agreement among tax experts that it was waseful and too costly. Top Carter administration policymakers opposed it in force.

Now the president finally has moved to counter the tax credit plan, and his strategy appears to some to be an equally classic example of how to throw bad money after bad tax breaks.

To many analysts, the step Carter has proposed -- to extend existing federal college scholarship programs to middle-income and upper-middle-income students --contains almost as many flaws as the tax credit provision itself.

Moreover, some critics fret it may have set in motion a dangerous race to see which side can get to the congressional finish line first. And judging by the past month's first lap, it could end up in a costly tie.

What Carter hoped to do was to head off the tuition credit by offering an alternative that would please its major constituency --middle-income and upper-middle-income families who are faced with large tuition bills.

Officials also wanted to enlist as allies the education lobby and key House and Senate education committee members. With these forces behind them, the counterattack might have a chance, top aides figured.

The proposal is a simple one: Instead of enacting the tax credit expand the current scholarship and work-study programs to make middle-income families eligible for benefits. (Before, only the poor could qualify.)

The plans seemed attractive from several angles. Policymakers justified it as "less wasteful" than the tax credit because it would not fritter benefits away on super-inch families. The tax credit is open to all.

Most important, expanding the scholarship programs would draw the support of the House and Senate education committees and the major education lobby groups, which both have a stake in retaining control of student aid.

Supporters lost no time in pointing out that, if the education panels didn't back the president's approach, they'd be giving up several billion dollars in jurisdiction to the congressional tax-writing committees.

The strategy worked -- to a point. Almost immediately after the president announced his aid proposal, the plan was endorsed by most of the big education lobbies. And Senate and House education leaders promised prompt action.

The problem was, the administration didn't count on the strength of the tax-credit forces. Not only are they continuing to press their case undaunted, but they may well come out ahead, to boot.

To begin with, the alternative the administration chose has left it vulnerable from a policy standpoint: Except for denying benefits to the few really wealthiest families, the plan has the same drawbacks as the credit.

There are these comparisons:

Officials complained last autumn that the tax credit would spend $1.3 billion to provide breaks of $250 a student -- hardly enough to do parents much good. Carter's plan would cost $1.4 billion -- for much the same benefits.

The White House blasted the tuition credit for benefitting taxpayers in the $20,000 to $40,000 brackets who it said didn't need a break. Carter's plan would do the same -- with scholarships rather than tax credits.

While the tax credit does waste benefits on some very-well-off families, the scholarship programs have been rife with red tape and large numbers of defaults. Officials have just begun to try to deal with that situation.

Finally -- and perhaps most important, from a political standpoint -- the president's new proposal has left him without the most telling line of defense against a tuition tax credit: that it simply is not justified.

Almost as soon as Carter unveiled his scholarship plan, proponents of the tuition credit sarcastically praised him for "finally recognizing" that this kind of aid is needed. No longer can the credit be dismissed as just a cover for general tax relief.

As a result, perhaps expectedly, while Carter's new plan may have the support of the education establishment, it hasn't dampened pressure for the tuition tax credit --gressional tax committees.

During last week's of hearings on the tax credit proposal, members of the House Ways and Means Committee indicated they still generally favor the tax credit plan, and are skeptical of enlarging existing scholarship programs.

And yesterday, the Senate Finance Committee voted overwhelmingly to tack the tuition credit onto a minor tax bill in time to send it to the floor for a vote sometime in the next few weeks.

Significantly, the Finance Committee bill eventually would allow the tax credit for elementary and high school tuition costs -- for an ultimate tab of $4.5 billion with strong support from the Catholic school lobby, the new combination package may prove unstoppable.

When Carter announced his new scholarship proposal a few weeks ago, he warned that the administration would "not accept" both the tuition credit and the increased grant program -- implying he would veto whichever came in last.

As it stands now, onlookers say it may mean Carter will have to veto his own scholarships alternative. And some critics are asking whether, in retrospect, it wouldn't have been easier to deal with only one dubious bill instead of two.