WASHINGTON — The bleak jobs report on Friday predictably had heads snapping toward the White House, looking to President Obama to do something. Yet his proposed remedies only underscore how much the president, just five months before he faces voters, is at the mercy of actors in Europe, China and Congress whose political interests often conflict with his own. That day, Mr. Obama continued his weekly travels around the country, prodding Congressional Republicans to pass his ”to-do list” of temporary tax cuts and spending initiatives to help create jobs. The Republicans only mock him, which leaves Mr. Obama free to blame his opponents and their presidential standard-bearer, Mitt Romney. But in doing so, he telegraphs a message of powerlessness that no leader likes to convey — least of all one who ran for office four years ago vowing to bridge Washington’s partisan gulf.