* Obama calls Republican plan "out of balance"
* Infighting among Republicans surfaces, Boehner offer criticized
* Coach advances dividend pay date to Dec. 27
* MetroPCS off as Sprint unlikely to make counter-offer
* Dow up 0.1 pct, S&P flat, Nasdaq off 0.1 pct
By Chuck Mikolajczak
NEW YORK, Dec 4 (Reuters) - U.S. stocks fluctuated between small gains and losses on Tuesday after remarks by President Barack Obama on budget talks dented optimism a solution could be found to prevent the economy from falling into recession.
Obama rejected a Republican proposal to resolve a looming fiscal crisis as "still out of balance" and said any deal must include a rise in income tax rates on the wealthiest Americans.
Obama spoke in an interview with Bloomberg Television.
Republicans in Congress proposed steep spending cuts to bring down the budget deficit on Monday but gave no ground on Obama's call to raise tax rates on the rich. The proposal was quickly dismissed by the White House.
"We have more of the same and what that really means is that you see very public negotiations that seem to be going nowhere," said Peter Kenny, managing director at Knight Capital in Jersey City, New Jersey.
"If there was any conviction that this was going to be a done deal, that we are going to see some really positive resolution on this fiscal cliff, you would see some real activity in the market."
The market has been sensitive to rhetoric from Washington, and many investors still expect the two sides eventually will reach a deal before the year's end, which could trigger a rally in equities.
Obama meets with U.S. governors at the White House on Tuesday to talk about the fiscal cliff, a $600 billion package of tax hikes and federal spending cuts that would begin Jan. 1.
Volume was light, with about 3.34 billion shares traded on the New York Stock Exchange, NYSE MKT and Nasdaq.
Differences within the Republican Party over how to engage with the Democrats came to the fore on Tuesday as one senator opposed to raising taxes lashed out at House Speaker and fellow Republican John Boehner for proposing to increase revenue by closing some tax loopholes.
Despite the sudden moves in the market, a measure of investor anxiety has held surprisingly flat.
The CBOE volatility index, a gauge of market anxiety, was at 17.36 but has not traded above 20 since July following its 2012 high near 28 hit in June. The VIX's 10-day Average True Range, an internal volatility measure, is at its lowest since early 2007.
Coach became the latest company to advance the date of its next dividend payment. Expectations of higher taxes on dividends kicking in in 2013 have pushed many companies to pay special dividends this year or advance their next pay-back to investors. Shares of the upscale leather-goods maker declined 2 percent to $57.06.
The Dow Jones industrial average added 16.60 points, or 0.13 percent, to 12,982.20. The Standard & Poor's 500 Index dropped 0.27 point, or 0.02 percent, to 1,409.19. The Nasdaq Composite Index dipped 3.81 points, or 0.13 percent, to 2,998.39.
Darden Restaurants Inc plunged 10.3 percent to $47.04 as the worst performer on the S&P 500 after warning its latest quarter would miss expectations after unsuccessful promotions led to a decline in sales at its Olive Garden, Red Lobster and LongHorn Steakhouse chains.
In contrast, Big Lots Inc surged 13.8 percent to $31.95 after the close-out retailer posted a smaller-than-expected loss and boosted its full-year adjusted earnings forecast.
Toll Brothers shares gained 1.1 percent to $32.80 after the largest U.S. luxury homebuilder reported a higher quarterly profit and said new orders rose sharply.
MetroPCS Communications shares tumbled 7.2 percent to $10.00 after Sprint Nextel appeared unlikely to make a counter-offer for the wireless service provider.
Shares of Pep Boys-Manny Moe and Jack slid 13.5 percent at $9.24 a day after the release of the auto parts retailer's results.