Will next month's tax cut help US economy to sizzle - or just fizzle?

White House officials are marking July 1 as something of a red-letter day on their calendars, with the hope that it may spark a consumer-led pullout from the present economic morass.

On that day, millions of Americans will begin to have a bit more cash in their pockets to save or to spend. Social security payments will climb by 7.4 percent, giving 36 million Americans a monthly increase ranging roughly from $25 to $75.

The withholding tax on wages and salaries of working Americans will shrink by about 10 percent, as the second installment of President Reagan's three-year income tax cut program takes effect.

Cumulatively, all this adds up to $45 billion of potential buying power spread over a year -- $33 billion in lower income taxes and $12 billion in higher social security benefits.

Treasury Secretary Donald T. Regan estimates ''roughly 50 percent of this will be saved or invested, 50 percent spent.

''If so,'' he told reporters, ''the businesses to recover first should be chain stores, soft goods, white goods, then household durables.''

Retail sales, or consumer spending, are especially important at this time, because two ingredients that usually help lead the nation out of recession are absent.

The construction industry, normally a harbinger of recovery, remains hobbled by high interest rates. Business spending for modernization also is down, because many firms are paying off heavy short-term debt and have little capital left for investment.

''Business balance sheets and corporate liquidity,'' says Allen Sinai of Data Resources Inc., ''are more fragile than at any other time in the postwar period.''

Housing will recover, analysts agree, only when the interest rate on construction loans -- now well above the 16.5 percent prime rate -- drops to 14 percent or below, and when mortgage interest rates also decline.

Housing starts in May rose 22 percent above the April level, reaching the highest monthly mark since July 1981. Analysts welcomed the construction growth, but said it was too early to predict how enduring the improvement might be. Much of the increase, was in multifamily, or apartment, units. This upsurge stemmed partly from the release of federal funds to build 70,000 subsidized units.

A boom in car sales likewise awaits lower interest rates, though as Mr. Regan noted, ''the fleet is aging, so the demand for new cars is there.''

All this means that the speed and duration of recovery will depend, to an unusual degree, on the extent to which American families spend their extra money.

Social security benefits are not taxed, so the 7.4 percent increase is a clear gain for elderly Americans. For most working Americans, the 10 percent income tax cut will be offset wholly or partly by two other factors.

Social security taxes are higher this year than last -- a maximum of $2,170. 80 compared with $1,975.05 in 1981. Also, cost-of-living wage hikes will thrust many Americans into higher income tax brackets -- a phenomenon known as bracket creep.

The extent of this higher tax burden, however, will become apparent to many Americans only when they make out their 1982 returns next spring. For the moment , families presumably will focus on the fact that their monthly take-home pay is a bit higher, beginning in July, than it had been.

But consumers alone cannot sustain an expansion, experts agree. Interest rates still must come down, allowing interest-sensitive industries like housing to perk up,

No one can be sure how far interest rates will drop if Senate and House finally agree on a fiscal 1983 budget that points toward lower, rather than higher, budget deficits in the coming years.

Almost all experts agree, however, that without a credible federal budget, both deficits and interest rates are likely to continue their climb.