Stock prices plunged today in heavy trading, with some Wall Street investment specialists suggesting that the move was part of a significant market downturn based on concerns about the national economy.

The Dow Jones Industrial Average fell by almost 23 points to 1030.17, adding to Friday's drop of nearly 18 points. Today's loss was the sharpest for that market indicator in three months.

Almost nothing was spared in the decline as losers outnumber gainers by 10 to 1 on the New York Stock Exchange. Only two of the 30 stocks that make up the Dow industrial average rose in the heavy trading, which totaled 90.8 million shares, up from 77.1 million Friday. Among the heavily traded losers were the blue chips that had led last autumn's rally, American Telephone & Telegraph, Exxon, General Electric and Procter & Gamble, for example.

"I think that the emphatic way with which the market came down today indicates that it has further to run down before beginning any meaningful rally," said Dana Stewart, market analyst for Bear, Stearns & Co.

"The interest rate rally has just about run its course and, with recovery now being forecast for the end of the year, that's too far ahead for stocks to anticipate better earnings," said William LeFevre of Purcell, Graham & Co. Inc.

Most market watchers have been predicting for some time that the record-setting stock surge that began five months ago had left many key blue-chip stocks overpriced--the Dow industrial average had soared 315 points in that period. As a result, a pullback from the all-time industrials high of 1092, set Jan. 10., was inevitable.

The fall of more than 40 points in the Dow industrials since Friday suggests that the "correction" they had forecast is well underway, but that, as bullish analysts see it, a new rally is likely to begin once the average falls below the 1,000 mark.

Several analysts also speculated that investors, worried about deficit projections, are watching particularly for indications of new spending cuts in President Reagan's State of the Union message on Tuesday.

Oil stocks were hit particularly hard today in light of the failure of ministers of the Organization of Petroleum Exporting Countries to agree on oil pricing and production. For example, Standard Oil of Indiana fell 4 3/8 to 40 5/8, Getty Oil fell 3 3/4 to 55 and Standard Oil of California fell 2 3/4 to 32 1/4.

The New York composite index fell 2.26 points to 80.92, and the average price per share there fell by 91 cents.

On the American Stock Exchange, only 73 stocks rose, while 670 declined as trading jumped from 7.4 million Friday to 9.8 million today. The Amex index fell 13.13 points to 352.45.