* Fed buys $5.56 billion in notes due 2017-18
* Debt ceiling debate starts to gain focus, may boost bonds
* Fed Chairman Bernanke to speak on Monday
By Luciana Lopez and Karen Brettell
NEW YORK, Jan 11 (Reuters) - U.S. Treasuries prices gained in choppy trading on Friday as investors struggled to find a new range for the debt, weighing a brighter economy against impending Washington budget battles.
Yields have largely stabilized after jumping last week on hints of growing unease within the Federal Reserve on the bank's asset-buying program.
"It's been quite a back and forth roller coaster today," said Justin Lederer, Treasury strategist at Cantor Fitzgerald in New York. "I think the market holds in here, I don't expect a major selloff overall. I think we remain rangebound for some time."
Yields for benchmark 10-year U.S. government debt could trade within a range of about 1.75 percent to 1.97 percent in coming sessions, Lederer said, with a break above 2 percent possibly signaling a further move upward.
Benchmark 10-year notes were last up 10/32 in price to yield 1.864 percent, from 1.90 percent late on Thursday.
Yields are down from a high of 1.98 percent last Friday, though they have increased from around 1.70 percent at year-end.
Until markets get lasting resolution on budget worries in Washington, analysts say investors could be wary of staking out positions.
Policymakers are slugging it out over how to cut federal spending, reduce the deficit and raise the debt ceiling. Those discussions will almost certainly be contentious - the August 2011 round of debt ceiling debates saw the U.S. credit rating cut from its sterling AAA by Standard & Poor's.
That potential for political acrimony, in turn, is fueling a safety bid that's keeping yields down, even as some investors see the trend for yields as still pushing higher.
"Overall, it does feel like rates would like to go higher," said James Newman, head of Treasuries and agency trading at Keefe, Bruyette and Woods in New York. But he noted that "the debt ceiling got in everyone's head, how that will play out."
Investors will closely watch a scheduled speech by Fed Chairman Ben Bernanke on Monday at the University of Michigan for any further indications of how long the Fed's latest bond purchase program will last.
"He's not speaking off a prepared text, so it's hard to see that he will use this speech as a vehicle to deliver any change in policy," said Yelena Shulyatyeva, U.S. economist with BNP Paribas. "But we will clearly be watching closely."
The Fed bought $5.56 billion in notes due 2017 and 2018 on Friday as part of its latest quantitative easing program, and it has scheduled Treasuries purchases for every day of next week.
Treasuries firmed earlier on Friday after an acceleration in China's consumer inflation rate narrowed the scope for further monetary easing in China, causing selling pressure in stock markets and supporting safe-haven instruments such as U.S. debt.
"We had ... disappointing inflation data out of China and the European equity market has run out of steam this morning - maybe a bit of profit-taking, consequently Treasuries have recouped some of their losses," said RIA Capital Markets bond strategist Nick Stamenkovic.