* Chicago PMI index at highest in January since April * U.S. jobless claims bounce off 5-year low * Nonfarm payrolls data awaited on Friday By Luciana Lopez NEW YORK, Jan 31 (Reuters) - Prices for U.S. Treasuries seesawed on Thursday after the Fed said it would continue buying bonds as the economy temporarily stalled, but uncertainty about growth in the world's biggest economy kept yields within recent ranges. Investors were also looking ahead to key nonfarm payrolls data on Friday, which could shed more light on whether jobs are growing fast enough to satisfy policymakers. Data on Thursday painted a mixed picture of the U.S. economy, with jobless claims bouncing off five-year lows to levels consistent with modest job growth. However, the pace of business activity in the U.S. Midwest picked up in January from a more than three-year low the month before as new orders jumped. Yields for 10-year Treasuries continued testing the 2 percent level, as they have since Monday, but found traction difficult to get. While the easing of global stresses, including the euro zone sovereign debt crisis, means that "people aren't really desperate to own Treasuries," there are still plenty of question marks keeping investors cautious, said Kim Rupert, managing director of global fixed income analysis at Action Economics LLC in San Francisco. From the possibility of automatic spending cuts kicking in at the start of March to lingering worries that the Fed will at some point cut off its easing spigot, investors are reluctant to push Treasuries outside recent ranges, she said. "We're still just trying to get a clean reading, but it doesn't look like growth is going to pick up substantially anytime soon," she said. Ten-year Treasuries are likely to see yields within the range of around 1.70 percent to 2.10 percent in coming sessions, said William O'Donnell, head of U.S. Treasury strategy at RBS Securities in Stamford, Connecticut. Recent higher yields have lured some investors back into buying, he said. "I think people like the levels." Thursday's data came after the U.S. Federal Reserve ended a two-day meeting on Wednesday by leaving in place its $85 billion per month asset buying program as the economy was paused. Ten-year notes traded 1/32 lower to yield 1.994 percent, from 1.992 percent late on Wednesday. Thirty-year bonds traded 4/32 lower to yield 3.187 percent from 3.1822 percent late on Wednesday. After a week packed with economic data - including disappointing fourth-quarter GDP figures - and the Fed meeting, investors are now turning to the last major milestone of the week: nonfarm payrolls on Friday. The Fed wants the unemployment rate to drop closer to 6.5 percent, but analysts in a Reuters polls see the unemployment rate staying at the current 7.8 percent.