In February, President Reagan proposed a budget containing a string of the largest federal deficits in history. Last week he told television and radio audiences that he supported a constitutional amendment to require a balanced budget.

Can he be serious?

The president is not the only one who has turned to this idea as deficit projections have soared. There are resolutions pending in both houses of Congress to amend the Constitution to limit revenues and spending and "require" a balanced budget, unless a two-thirds majority of both houses votes for a deficit.

But this interest in a constitutional amendment is less a sign of politicians' determination to balance the budget than of their near helplessness in the face of ballooning deficits in coming years. As Federal Reserve Chairman Paul A. Volcker observed yesterday, "The current budgetary debate provides an acid test of the will of the Congress . . . A vote for a future amendment seems to me not nearly so meaningful as action now," even if it is appealing as a painless way of voting for a balanced budget.

There are many other objections to the notion of a balanced-budget amendment.

First, it is very unlikely that such an amendment could achieve its stated goal of balancing the budget, certainly not without distorting the machinery of government and making a major shift in the balance of power between Congress and the president.

The resolutions now under consideration, and supported by Reagan, would require Congress and the president to present a statement each year in which outlays do not exceed receipts and then to ensure that actual outlays do not exceed those in the statement. In addition to balancing the budget, they aim to limit spending and taxes by tying the allowable increase in revenues to the increase in total gross national product in the previous year.

There is, however, no requirement that actual receipts match those in the statement. Moreover, the amendment neither explains how the outlays statement should be enforced nor, of course, solves the difficult choices of what particular spending or tax measures should be passed if there is a deficit in prospect that Congress does not approve.

Many experts believe that it would be impossible to deal with unpredictable spending demands --for example, because of lower-than-expected farm prices, a natural disaster, or an unexpected rise in interest rates--unless Congress were to give the president enormous power to alter spending programs as necessary.

Second, it is likely that if the federal government were constitutionally deterred from spending more, it would try to achieve its objectives by other less efficient, and less visible, means.

For example, credit programs may be substituted for spending programs, with favored activities encouraged by loan guarantees or subsidized credit rather than government spending. And pressure groups could seek to redefine the budget, perhaps by taking Social Security out of it.

Another argument against a balanced-budget amendment is that fiscal policy should be flexible enough to respond to current economic conditions, and a balanced budget often may not be appropriate.

Finally, while it is clear that the president and other conservatives backing the balanced-budget and tax-limitation amendment hope it would reduce the role of government, it is less clear that this political judgment today should be enshrined in the Constitution.

Reagan's budget director, David Stockman, claimed yesterday that "a consensus is building" that it is "inconsistent with long-term economic health" to have federal spending or revenues equivalent to more than 20 percent of the total economy, or GNP. But many economists and politicians would challenge that claim.

Professional economists do not agree that economic forces dictate a certain optimal size for the federal government. At different times and in different countries, the government's importance has varied considerably, with no clear corresponding change in economic health.

As society's values change, so does the appropriate size of the federal government. There is little reason to think that the Constitution should build in a particular level rather than leaving this judgment to successive lawmakers. Indeed, the success so far of Reagan's efforts to slow the growth of nondefense federal spending shows that Congress can change this in response to political pressure.

The present deficit problem has come largely because Congress voted a big tax cut without reaching a consensus on whether and how to cut spending to match. "Should stalemate ensue in 1982," Robert Hartman of the Brookings Institution wrote, "the blame should rest more on the failure to reach a consensus on how much the federal government should tax and spend than on a shortcoming of the budgetary process." A constitutional amendment cannot create consensus where there is none, but just a different form of stalemate.