The Dow Jones industrial average, ignoring the budget crisis in Washington, slipped a mere 6 points yesterday after a day of volatile trading.

Within minutes of the opening bell at the New York Stock Exchange, the Dow plunged 59 points as a tidal wave of computerized program trades hit the floor and traders braced for a strong reaction to the House vote rejecting the budget compromise.

Declines inundated advances on the Big Board by an extreme 13-to-1 ratio, and a number of stocks could not open because so many shares were offered for sale.

But after the initial slide, a spirited rebound took hold as institutional investors moved in to pick up bargains.

Stefan D. Abrams, investment strategist at Kidder, Peabody & Co., spoke for much of Wall Street when he surveyed the budget chaos in Washington and declared, "All you're looking at today is political gamesmanship."

Robert T. Mikkelsen Jr., a senior vice president at Lehman Brothers in New York, agreed. "A lot of people think this {budget problem} will be worked out over the weekend ... although obviously they're going to march it right down to the wire."

The market also took in stride the Labor Department report showing a net loss of private sector jobs in September, and another $1.06 runup in the price of oil. A barrel of crude for November delivery traded at $37.99 on the Mercantile Exchange.

As with stocks, bonds ended the day little changed after a shaky opening. The dollar was mixed against various currencies, plunging against the pound on news that Britain would join the European currency system, but regaining ground against the German mark.

At the close, the Dow stood at 2510.64, down 6.19, while declines led advances by a 901-to-586 margin on volume of 153 million shares.

General Motors rose 1 1/4 to 36 7/8 on favorable publicity for its new Saturn car and improved prospects for signing a contract with its Canadian workers.

Insurance issues generally were undermined by news that Travelers Corp. will cut its dividend and report a $500 million loss for the third quarter because of problems with its real estate portfolio. Travelers stock closed down a hefty 4 3/8 at 16 3/8, while Aetna tumbled 3 3/4 to 33 5/8, Cigna gave up 2 3/4 at 36 1/8, and Transamerica lost 1 3/4 to 24 3/4. Among the property and casualty insurers, Chubb Corp. dropped 1 3/4 to 36 3/4, USF&G Corp. skidded 1 3/4 to 15 1/8 and Continental fell 1 1/2 to 19 3/8.

The Dow transports eased 2.96 to 866.32, led by UAL Corp., which dropped another 2 5/8 on news that Chairman Stephen Wolf had sold most of his options in the stock. Utilities firmed 0.50 to 205.42.

Among broad stock indexes, the Standard & Poor's 500 finished down 1.19 at 311.50, the NYSE Composite was down 0.63 at 170.70, the Value Line dropped 0.77 at 229.12, the Amex Market Value was down 1.66 at 306.48 and the Nasdaq Composite fell 2.53 at 347.36.