* Texas Instruments forecast boosts tech shares
* 3-year Treasury note auction on tap
* Nasdaq up 0.6 pct, S&P 500 up 0.03 pct; Dow down 0.2 pct
* For up-to-the-minute market news click [STXNEWS/US] (Updates to midday, changes byline)
By Rodrigo Campos
NEW YORK, June 9 (Reuters) - The Nasdaq rose on Tuesday after Texas Instruments raised its outlook, but other indexes were flat to lower after plans by big banks to repay a government bailout raised questions about whether the move would help the recovery.
Stocks initially rose after the Treasury Department said 10 big banks will pay back $68 billion to the government, but quickly fell back on concerns they might be diverting money they could be lending to boost the economy.
Investors switched their attention to a 3-year Treasury note auction set for 1 p.m. EDT, (1700 GMT) with markets worried that an oversupply of government debt could push interest rates still higher and increase the cost of borrowing to consumers and businesses.
"It's one of the biggest things driving the market recently. It is a market-moving event that we'll be paying close attention to," said Bennett Gaeger, managing director at Stifel Nicolaus in Baltimore.
The Dow Jones industrial average <.DJI> dropped 18.51 points, or 0.21 percent, to 8,745.98. The Standard & Poor's 500 Index <.SPX> gained 0.24 points, or 0.03 percent, to 939.38. The Nasdaq Composite Index <.IXIC> rose 10.92 points, or 0.59 percent, to 1,853.32.
Shares of Texas Instruments Inc
The PHLX semiconductor index <.SOXX> gained 3.5 percent.
"Any time you get a company discussing guidance and increasing guidance, its going to be taken as out-sized positive news," said Dan Greenhaus, an analyst at Miller Tabak & Co.
General Electric Co
The S&P 500 <.SPX> has rallied 39 percent since hitting a 12-year closing low on March 9, leading analysts to speculate a correction was looming, although recent dips have been short-lived.
(Reporting by Rodrigo Campos; additional reporting by Edward Krudy; editing by Jeffrey Benkoe)