* Non-farm payrolls jump 236,000 in February * Unemployment rate falls to 7.7 percent from 7.9 percent * Average hourly earnings rise four cents, workweek up * Report shows underlying strength in the economy By Lucia Mutikani WASHINGTON, March 8 (Reuters) - U.S. employers added a greater-than-expected 236,000 workers to their payrolls in February and the jobless rate fell to a four-year low, offering a bright signal on the economy's health. The data from the Labor Department on Friday showed the economy gaining traction. The unemployment rate fell to 7.7 percent, the lowest since December 2008 as more people found work and others gave up the hunt. Economists welcomed the report, but worried that government budget tightening in Washington could slow the recovery's momentum. "We had already moved from a slog to a jog and we are on course to really get rolling. The risk here is, while the economy is gathering speed, the politicians are stepping on the brakes," said Bill Cheney, chief economist at John Hancock Financial Services in Boston. A 2.0 percent payroll tax cut ended and tax rates went up for wealthy Americans on Jan. 1, and $85 billion in federal budget cuts started taking effect on March 1. The employment report, which showed broad-based job gains, was just the latest sign of the economy's fundamental health, and it added fuel to a rally in U.S. stocks that had already propelled the Dow Jones industrial average to record highs. The Dow scaled another closing high and the Standard & Poor's 500 index rose for a sixth straight day on Friday. The U.S. dollar raced to a 3-1/2 year high against the yen and touched a three month peak against the euro. The yield on the benchmark 10-year U.S. Treasury note hit an 11-month high around 2.08 percent. While payrolls growth beat economists' expectations for 160,000 jobs, it was not seen as a game changer for the Federal Reserve, which has pumped more than $2.5 trillion into the economy to foster faster growth. "It's a first step down a long road before the Fed is convinced we are really we are seeing a substantial improvement in labor market conditions," said Michael Hanson, a senior economist at Bank of America Merrill Lynch in New York. "They will want to see 200,000 job growth, not just in one month, but several months in a row. The unemployment rate is still too high." The central bank is buying $85 billion in bonds per month and has said it would keep up its asset purchases until it sees a substantial improvement in the labor market outlook. It is likely to remain leery of withdrawing its support too soon given the tightening of fiscal policy. A Reuters survey of the 17 large financial institutions that deal directly with the Fed found that they all expected it to continue bond purchases until at least late this year. Eleven expected the program to continue into 2014. Although December and January's employment data was revised to show 15,000 fewer jobs added than previously reported, details of the report were solid, with construction adding the most jobs since March 2007 and hours for all workers increasing. STILL AMPLE SLACK The pace of hiring in February marked an acceleration from the 195,000 per month average of the prior three months, and it approached the roughly 250,000 jobs per month economists say are on a sustained basis to significantly reduce unemployment. Still, employment remains three million jobs below the peak reached in January 2008. Highlighting the need for faster employment growth, the share of the work age population with a job was unchanged at a historically low 58.6 percent for a third straight month, a reminder of the immense slack that remains in the labor market. In addition, the report showed that in February the jobless experienced longer periods of unemployment. Last month, construction employment increased by 48,000 jobs after rising by 25,000 in January. The housing market has turned around decisively and employment is also being support by rebuilding on the East Coast after the destruction by Superstorm Sandy in late October. Manufacturers also stepped up hiring. Factory jobs increased 14,000 last month after rising 12,000 in January. Retail employment increased by 23,700 jobs, an eighth straight monthly gain that defied a recent slowdown in sales. Healthcare and social assistance saw another month of solid job gains. The same was the case for the leisure and hospitality industries. Government continued to shed jobs. Public payrolls dropped 10,000 last month after falling 21,000 in January. The sustained steady job gains are lending some stability to wages. Average hourly earnings rose four cents last month. That was the fourth straight monthly gain. Earnings were up 2.1 percent in the 12 months through February, rising for by the same margin for a third month in a row. "This provides a significant offset to the multitude of headwinds plaguing the consumer in the first quarter and suggests spending could do a bit better than anticipated," said Tom Porcelli, chief U.S. economist at RBC Capital Markets in New York.