U.S. stocks stayed near the break-even point on Tuesday as persisting worries about overseas fiscal problems offset optimism over data that underscored the view the economy was stabilizing.

Consumer confidence and housing data pointed to an improving economy, bolstering sentiment ahead of Friday's key payrolls report from the government.

But trading volumes were light, with Passover and the upcoming Easter holiday taking participants away from the market, traders said.

Volume is light ... and it seems like the market is just kind of hanging in there. We're getting close to the 11,000 level on the Dow, said Todd Leone, head of listed trading, Cowen & Co. in New York.

Giving the market a lift was Apple Inc , whose move to develop a new iPhone buoyed telecom and chipmaker shares. Apple's stock was up 1.2 percent at $235.15.

Financials kept the S&P 500 under pressure, with Bank of America shares down 1.6 percent at $17.76.

Worries about Greece's funding needs lingered a day after an auction of 7-year Greek bonds drew weaker demand than hoped for by some.

The Dow Jones industrial average <.DJI> was down 9.60 points, or 0.09 percent, at 10,886.26. The Standard & Poor's 500 Index <.SPX> was down 1.85 points, or 0.16 percent, at 1,171.37. The Nasdaq Composite Index <.IXIC> was down 1.41 1.63 points, or 0.06 percent, at 2,402.95.

I think there's more to the issue of sovereign debt and bond yields than people make out, said Subodh Kumar, chief investment strategist of Subodh Kumar & Associates, in Toronto.

The major indexes are set for gains as the first quarter draws to an end with Wednesday's close.

For the first quarter so far, the Dow is up 4.54 percent, while the S&P 500 is up 5.2 percent and the Nasdaq is up 5.98 percent.

Apple shares shot to a record high intraday of $237.48. The stock climbed after a Wall Street Journal report that Apple is developing a new iPhone that would work on Verizon Communications Inc's mobile network.

Verizon was up 2.6 percent at $31.24.

On the economic front, U.S. consumer confidence rebounded in March, as optimism about the labor market increased slightly, the Conference Board said.

Earlier data on Tuesday on January home prices also pointed to stability in the U.S. housing market. The Standard & Poor's/Case-Shiller home price index showed home prices rose in January for the eighth straight month, with the best annual rate in nearly three years. Year over year, home prices dipped, the January reading showed.

March non-farm payrolls are scheduled for release Friday morning even though the stock market will be shut for the Good Friday holiday.

(Reporting by Caroline Valetkevitch; Additional reporting by Angela Moon; Editing by Jan Paschal)