* U.S. to hold $24 billion 3-year note auction
* Stocks wobble ahead of Trump's news conference
* U.S. small business optimism hits 12-year peak
By Richard Leong
NEW YORK, Jan 10 (Reuters) - U.S. Treasury yields were little changed on Tuesday as investors made room for $24 billion of three-year government notes, which was offset by appetite for bonds due to a pullback in U.S. stocks.
Bond yields have held in a tight range following last Friday's jobs data that showed the U.S. labor market continued to tighten and a tentative pickup in wage growth.
"It's a market that's trying to sell off but it's not succeeding," said Aaron Kohli, interest rates strategist at BMO Capital Markets in New York.
The yield on benchmark 10-year Treasuries was little changed at 2.378 percent after moving in a narrow 3 basis-point range.
Two-year yields were flat at 1.194 percent, while 30-year yields edged up 1 basis point to 2.978 percent.
In "when-issued" activity, traders expected the latest three-year Treasury supply to sell at a yield of 1.481 percent, compared with 1.452 percent at the prior three-year note sale.
Data that showed U.S. small business optimism hit a 12-year high in December revived the notion that the domestic economy may pick up steam with possible stimulus programs from the incoming Trump administration and a Republican-controlled Congress.
More spending and investments could result in a swifter pace of interest rate increases from the Federal Reserve to keep inflation under control.
Possibility of steep tax cuts and infrastructure spending has stoked worries about a surge in federal borrowing, traders and analysts said.
"The market will remain cautious, particularly longer-dated issues, with concerns about Treasuries issuance which may accelerate inflation," said Jason Celente, senior portfolio manager at Insight Investment in New York.
Investors awaited details about possible economic policies from President-elect Donald Trump who was scheduled for a news conference on Wednesday.
Wall Street stocks have retreated from their record levels as traders re-assess whether Trump can deliver the tax cuts and other economic issues he campaigned on.
The pullback in risk appetite has renewed some demand for Treasuries since the beginning of the year.
Speculators, however, are betting heavily that U.S. yields will climb higher in 2017. Fed officials have hinted they would raise short-term interest rates further after hiking them by a quarter point in December.
Speculative net shorts in five-year and 10-year Treasury note futures rose to record levels last week, according to data from Commodity Futures Trading Commission released on Friday. (Reporting by Richard Leong; Editing by Meredith Mazzilli)