In becoming the nation's top-rated cable news network, Fox News Channel was helped by millions of conservative viewers who tuned in to watch the likes of Bill O'Reilly, Tony Snow and Cal Thomas. But to win a ratings war in Washington, Fox-parent News Corp. is counting on the support of some unlikely allies: Democrats. News Corp. is quietly courting Democratic lawmakers on Capitol Hill to block a new local-TV ratings system that lowers ratings for many of its stations. The company contends the new ratings system, launched by Nielsen Media Research in four major television markets last year, greatly undercounts...