STOCK were mixed in choppy trading yesterday on the New York Stock Exchange as investors continued to contend with the fallout from the ongoing battle in Washington over refunding the federal debt. The US Government essentially went broke yesterday and began shutting down all but basic services. Congress, however, remained in session. The blue-chip Dow Jones industrial average, which added 2.53 points on Monday to its fourth consecutive record close, was ahead another 7.22 points to 4,880.12. The broader NYSE composite index was off 0.51 to 315.12, while Standard & Poor's 500-stock index was down 1.34 to 590.96. Prices were also lower on the Nasdaq stock market with the composite index down 6.24 to 1,052.22. Analysts said Wall Street continued to focus on the fight for a budget resolution, which was expected to dominate investors' attention during the session. Clinton administration officials yesterday took a gloomy view of the budget impasse, indicating there was no reason for optimism at this point.