SARATOGA SPRINGS, N.Y. — Only a few years ago, John E. Sweeney was a rising star in New York Republican circles, a streetwise political operative who helped engineer the 1994 victory of a little-known state senator, George E. Pataki, over Gov. Mario M. Cuomo before going on to take a seat in Congress. There, his combative brand of politics made him a favorite of national Republican leaders, including President Bush. But these days, with Congressional elections just six months away, Mr. Sweeney finds himself in the political battle of his life, as he faces his first significant electoral challenge since...