* Mid-Atlantic factory activity contracts in May * U.S. jobless claims rise sharply in latest week * Housing starts drop more than expected in April * Inflation data points to softer demand in economy By Jason Lange WASHINGTON, May 16 (Reuters) - The U.S. economy showed fresh signs of slower growth in the second quarter, with factory activity slipping in the mid-Atlantic region while groundbreaking declined at home construction sites. Other data on Thursday showed a spike in new claims for jobless benefits last week as well as soft underlying inflation that could point to weak demand in the economy. "We are seeing a soft start for growth in the second quarter," said Sam Bullard, an economist at Wells Fargo in Charlotte, North Carolina. The data could raise concerns over the impact of a government austerity drive that began in January and the fallout from a recession in the euro zone. It could also increase pressure on the Federal Reserve to keep its money printing press running on overdrive to support the economy. The Philadelphia Federal Reserve Bank said its gauge of factory activity in the mid-Atlantic region fell to minus 5.2 in May. Negative readings in the index point to a contraction in activity. Drops in new orders and in employment weighed on the index, which covers factories in eastern Pennsylvania, southern New Jersey and Delaware. The report added to recent signs that weakness in manufacturing in March and April extended into May. "We are not rebounding from the recent swoon," said Jacob Oubina, an economist at RBC Capital Markets in New York. "We are just muddling along." U.S. economic growth picked up in the first three months of the year after a dismal fourth quarter, but the April-June period is expected to show a more lackluster expansion as Washington's push to trim the budget deficit weighs on consumers and businesses. The federal government hiked taxes in January and initiated sweeping budget cuts in March. Signs of consumer weakness were evident in a report by Wal-Mart that sales fell 1.4 percent in the first quarter at its U.S. stores open at least a year. The data put downward pressure on U.S. stock prices, which were little changed at midday. It also pushed down yields on U.S. government debt, while the dollar weakened against a basket of currencies. SLOW STARTS Groundbreaking for new U.S. homes fell more than expected in April, plunging 16.5 percent to a 853,000-unit annual rate, the Commerce Department said in a separate report. Still, permits to build new homes rose, lending support to the expectation of analysts that housing will contribute to the economy's recovery this year. In addition, most of the weakness in starts was in the volatile multifamily homes segment. Separately, a report from the Labor Department showed a sharp drop in gasoline costs in April led to the biggest drop in U.S. consumer prices in more than four years. The Consumer Price Index slipped 0.4 percent, the biggest decline since December 2008 when America was suffering some of the darkest days of its financial crisis. Analysts had expected a more modest 0.2 percent drop. In the 12 months through April, consumer prices rose 1.1 percent. That is well below the Fed's 2 percent inflation goal. The U.S. central bank targets a different gauge of prices that tends to run cooler than the Labor Department's index. Gasoline costs plummeted by 8.1 percent, the biggest fall since December 2008. However, the weakness in the price index extended to a measure of underlying inflation that strips out volatile energy and food prices. That gauge rose just 0.1 percent, and was up only 1.7 percent from a year earlier - its smallest 12-month advance since June 2011. "Further falls in U.S. core inflation in the coming months may make some Fed officials concerned about very low inflation, or even deflation," said Paul Dales, an economist with Capital Economics in London. Deflation entails spiraling declines in prices and wages and is difficult for policymakers to combat. Inflation has held low in large part because of weakness in the labor market, which has kept a lid on wages and spending. Last week, the number of Americans filing new claims for unemployment benefits climbed at the fastest pace in six months, although analysts said one week's data was not enough to derail the labor market's slow but steady recovery. "If you get another week or two over 350,000, then you might be more concerned," said Craig Dismuke, chief economic strategist at Vining Sparks in Memphis, Tennessee.