* Indexes face technical resistance after 2 1/2 yr highs
* Private employers add more jobs than forecast-ADP
* Investors eye Egypt as protests persist
* Indexes: Dow flat, S&P down 0.1 pct, Nasdaq up 0.2 pct (Updates to midday; changes byline)
By Angela Moon
NEW YORK, Feb 2 (Reuters) - U.S. stocks seesawed between modest gains and losses on Wednesday as indexes struggled to move higher a day after the Dow and S&P 500 closed at their highest in about 2-1/2 years.
Investors were reluctant to make big bets on stocks even though data showed U.S. private employers added more jobs than expected in January.
"We are pushing into the technical resistance. They (indexes) have moved awfully far on the short-term, intermediate and even long-term basis," said Fred Dickson, chief market strategist at D.A. Davidson & Co in Oregon.
The Dow Jones industrial average was up 2.16 points, or 0.02 percent, at 12,042.32. The Standard & Poor's 500 Index was down 1.45 points, or 0.11 percent, at 1,306.14. The Nasdaq Composite Index was up 4.45 points, or 0.16 percent, at 2,755.64.
The Dow closed comfortably above the milestone 12,000 level for the first time since June 2008 on Tuesday and the S&P also closed above the psychological hurdle of 1,300 mark for the first time since August 2008.
Joseph Hargett, a strategist at Schaeffer's Investment Research, said the Dow needs to stay above 12,000 firmly as a short-term support.
"The resistance (for the Dow) now resides in the 12,100-12,200 area."
Investors kept an eye on the massive protests in Egypt as clashes erupted between opponents and supporters of President Hosni Mubarak. Concerns that protests would spread throughout the region have pressured equities in recent sessions.
The Market Vectors Egypt Index ETF which consists of shares of companies in Egypt, fell 5.6 percent to a session low of $17.48 after rising for two consecutive days.
In earnings news, appliance maker Whirlpool Corp dropped 4 percent to $82.06 after its profit missed estimates.
Time Warner Inc and Mattel Inc rallied after both companies reported stronger-than-expected quarterly profits. Media group Time Warner gained 6 percent to $34.24 while toymaker Mattel was up 1.5 percent to $24.52. (Reporting by Angela Moon, Editing by Kenneth Barry)