* Citigroup adjusted profit hit by bond trading slowdown; shares dip
* U.S. senators hint at possible fiscal deal on Tuesday
* NY factory growth slows in Oct to weakest since May -NY Fed
* Indexes down: Dow 0.4 pct; S&P 0.4 pct; Nasdaq 0.1 pct
By Angela Moon
NEW YORK, Oct 15 (Reuters) - U.S. stocks fell on Tuesday after a four-session rally as Citigroup reported weaker-than-expected quarterly earnings, overshadowing developments in the Washington budget and debt-limit talks.
Citigroup fell 1.1 percent to $49.06 after the third-largest U.S. bank reported earnings. The bank was hit by a double-digit drop in bond trading revenue after the Federal Reserve left its stimulus policies in tact in September and customer activity fell.
The S&P financial sector index was among the biggest decliners, down 1.3 percent.
The political standoff in Washington showed signs of giving way to a Senate deal to reopen federal agencies and prevent an economically damaging default on federal debt. The deadline to lift debt ceiling is Oct. 17.
U.S. Senate Majority Leader Harry Reid said he was confident that Senate Democrats and Republicans can reach a comprehensive fiscal agreement this week that avoids a U.S. default on debt and other obligations.
Signs of optimism are building and "investors are showing increasing signs of confidence that default will be averted," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co in New York.
House Republicans said they hope to pass a version of legislation to reopen the federal government that would differ from a plan now emerging from Senate negotiations.
In a busy day of earnings, nine companies representing 5.1 percent of the S&P 500 index report results including Yahoo! Inc and Intel Corp after the bell.
The Dow Jones industrial average was down 24.82 points, or 0.16 percent, at 15,276.44. The Standard & Poor's 500 Index was down 1.90 points, or 0.11 percent, at 1,708.24. The Nasdaq Composite Index was up 3.42 points, or 0.09 percent, at 3,818.69.
Johnson & Johnson reported stronger-than-expected quarterly results on strong growth for its prescription drugs. The stock was up 1.4 percent at $91.08.
Coca-Cola Co reported higher earnings and lower revenue, helped by strong global sales of its Coca-Cola brand products. But the stock was off 0.5 percent at $37.71.
Christopher Bailey, the designer credited with restoring the cachet to fashion brand Burberry, is to become chief executive next year when long-standing boss Angela Ahrendts will move to Apple.
Ahrendts, who has been Burberry boss for eight years, during which its share price soared about 250 percent, will take up a newly created position at Apple as a senior vice president with oversight of retail and online stores. She will report directly to CEO Tim Cook. While Apple shares were up 0.5 percent to $498.75, Burberry shares plunged 6.1 percent.
Shares of Teradata Corp fell 16.5 percent to $43.96, a day after the data analytics firm cut its full-year earnings forecast by about 10 percent.
Data showed the pace of growth in New York state's manufacturing sector slipped this month to its slowest since May, but business optimism stayed strong. The market's reaction was muted.