* Yields back off eight-month highs reached last week * Treasury sells $21 billion of 10-year notes * 30-year bond yields seen heading back toward 3 percent By Luciana Lopez NEW YORK, Jan 9 (Reuters) - Prices for U.S. Treasuries edged up on Wednesday, taking yields off last week's eight-month highs but still within recent ranges, as looming debt ceiling talks kept investors wary. Prices dipped briefly after a weak auction of $21 billion 10-year notes but recovered quickly. At 1.863 percent, the high yield for the auction exceeded market expectations, with lower-than-average non-dealer bidding and bid-to-cover. But analysts said the budget battle in Washington overshadowed the results of the sale, with investors unsure where the debate could go and what direction the market could take. "It's the debt ceiling. What's the fight going to look like, how much spending cuts are we going to get out of that, if any, and what is it going to mean," said David Ader, head of government bond strategy at CRT Capital Group in Stamford, Connecticut. "I think it's going to be a choppy and largely sideways and indecisive time until then," he said. Benchmark 10-year Treasury notes were trading 4/32 higher in price, their yield at 1.850 percent from late Tuesday's 1.87 percent. Yields on Friday touched 1.98 percent, the highest since late April. Yields have generally been easing since that Friday high after minutes from the Federal Reserve's December policy meeting sparked some worries the central bank could pare back its asset purchases sooner than expected if the economy improves enough. Also boosting yields last week, Republicans and Democrats reached a deal to soften an austerity package scheduled to kick in at the beginning of the year that might have pushed the economy back into recession. But the respite from that deal could be merely temporary, as the compromise only postponed major across-the-board spending cuts. In addition, the Treasury hit the $16.4 trillion limit on the amount of borrowing that is authorized by Congress on Dec. 31, and the United States would default on its debt within weeks unless Congress raises the limit. The last time policymakers squabbled over the debt ceiling, in 2011, the United States' AAA credit rating was cut by Standard & Poor's. With negative outlooks from all three major rating agencies, investors are worried that the U.S. credit rating could get dented further if no solution is reached. The Treasury has a $13 billion auction of 30-year bonds on Thursday. The sale of $32 billion of three-year notes on Tuesday drew strong non-dealer bidding. The high yield was 0.385 percent, in line with expectations. Thirty-year Treasury bonds were trading 8/32 higher in price, their yield at 3.053 percent from late Tuesday's 3.07 percent. Thirty-year bond yields on Friday rose to 3.18 percent, marking the highest since late April, and some analysts were calling for a further pullback in the yield.