CUYAHOGA FALLS, Ohio — Two presidential campaigns dealing with sudden reversals of fortune descended on this must-have state Tuesday, one hoping to sustain a new momentum, the other hoping to regain its footing.

In both rhetoric and demeanor, President Barack Obama and Republican Mitt Romney came to Ohio acutely aware of the altered terrain.

Romney, buoyed by new polls that show him pulling ahead of the president, has shed the languid pace that characterized his travels as recently as last weekend. He appears renewed, even ebullient, and so do his crowds. About 500 people endured a driving rainstorm and a muddy field to see him Monday evening in Newport News, Va., and an estimated 12,000 packed a parking lot for a Romney rally Tuesday night in Cuyahoga Falls, Ohio.