President Carter sent Congress yesterday a two-year, $31.2 billion economic stimulus program that his chief economic adviser said is "designed to tread prudently between the twin risks of over-and under-stimulation.

Charles E. Schultze, chairman of the Council of Economic Advisers, predicted that if the program is enacted, the unemployment rate, now 7.8 per cent, would drop to 6.7 to 6.9 per cent by the end of this year and around 6 per cent by the end of 1978.

Accompanied by Treasury Secretary W. Michael Blumenthal and Office of Management and Budget Director Bert Lance, Schultze explained and defended the program before the House Budget Committee.

He conceded that economic statistics since October "indicate that the recovery is proceeding once again," but argued that without a stimulus, expansion could not be self-sustaining. All three officials, however, warned Congress against any substantial boost in the overall Carter proposals.

"It is far easier to add more stimulus late in 1978, should that be needed, than to retract stimulus once committed," Schultze said.

The proposals followed, with minor exceptions, an outline released by Lance on Tuesday. The first year's program, $15.5 billion, is dominated by $11.4 billion in tax rebates, while the second year's program, amounting to $15.7 billion - with no tax rebates - shifts the emphasis heavily to public works and jobs programs.

As expected, the program ran into immediate opposition from liberal Democrats, who questioned the effectiveness of the tax rebat principle and demanded more spending more quickly on direct job programs. And Republicans were critical of the boosted federal deficit, which Blumenthal estimated would rise to $67 billion to $69 billion in fiscal 1977 from the Ford administration projection of $57.2 billion.

But the three Carter economic aides defended the pack age, saying the $1.7 billion planned for jobs-related spending programs in this fiscal year is all that could reasonably be achieved. "But this package is not the be-all and end-all of our (future) efforts to deal with the unemployment problem," Schultze assured the committee.

The tax rebate, Blumenthal said, is the only way to give the economy a quick stimulus that can boost consumer spending. Schultze disputed arguments that the 1975 rebate - about an $8 billion return of tax money - did not work.

"The problem (with the 1975 rebate) was that it didn't last long enough, and that's why our program has a continuing element in 1978," Schultze said.

The tax rebate will be provided, if Congress accepts the proposal, by a $50 check from the Internal Revenue Service to almost everyone in the United States, Assistant Treasury Secretary Laurence N. Woodworth estimated that 4 per cent of the population, or 8 million persons, would fail get a rebate while 206 million persons will covered.

Checks will be mailed, as a rebate taxes paid in 1976, on the basis of [WORD ILLEGIBLE] for the taxpayer, and each dependent. Thus, a married couple with two children would get $200. A couple with six children would get $400. There is no upper limit.

A payment of $50 will also go to Social Security recipients, those receiving supplemental security income payments and those getting railroad requirement benefits. Thus, there is a possibility of a "double dip," or two ret [WORD ILLEGIBLE] tes to a person, for example, who paid taxes last year and also received Social Security.

In most cases, for poor persons who had little or no tax liability, the government will still mail a $50 tax rebate for each dependent listed on a 76 tax form.

But some will not get a rebate. For example, a single person or a married couple without children (who are not eligible for an earned income credit under a 1975 tax law) and who had no tax liability, would not get a rebate. (They would, however, get a $50 payment if they are getting Social Security or other qualifying retirement benefits.)

Many of the 8 million excluded would be college students with no dependents who had no tax liability. In cases where parents also were entitled to claim a student as a dependent on their own returns, a rebate would be paid.

Officials pointed with satisfaction to the prospect of 96 per cent coverage, against 89 per cent for the 1975 tax rebate. The essential difference is that the rebate will reach everyone entitled to the earned income credit, which was not available in 1975.

Another important tax feature of the proposal is a permanent reduction of $4 billion, on an annual basis, for individuals, which would be accomplished by replacing the current law's standard deductions provisions with a flat $2,800 for joint returns.

Blumenthal called this proposal the first down-payment on a longer-term tax reform package being readied at the Treasury. It will provide $1.5 billion in tax relief this year and $5.5 billion for next year.

For married persons with incomes up to $17,500 and individuals with incomes up to $15,000, the more generous and simplified deductions will mean tax cuts of around $100 or more.

A family of four might expect to get tax benefits of around $300 this year - $200 in the rebate on last year's taxes, and $100 or more through the standard deduction change. Against that, the higher level of earnings taxable for Social Security purposes can cost a maximum of $70.20.

The change in the standard deduction, and a two-way option for business taxpayers, would be permanent parts of the tax structure. Together they total $6.5 billion, which Schultze said avoids "mortgaging future revenues or endangering the ultimate goal of balancing the federal budget."

Business owners would get the option of an additional 2 per cent investment tax credit (making it 12 per cent), or a refundable 4 per cent credit against income taxes, based on the amount of their payroll taxes going into the Social Security trust fund.

The full-year effect of the business tax cut is estimated at $2.6 billion, of which $1.5 billion would be the revenue lost to the higher investment tax credit, and $1.1 billion for the Social Security credit.

Blumenthal, former Treasury Secretary William E. Simon's repeated warning that enlarged government deficts "crowd out" private borrowers in the financial markets, said that there would be adequate funds to meet total credit market demands - public and private - of nearly $300 billion in this calendar year. "We are unlikely to be confronted with a situation of 'crowding out,' Blumenthal said.