Top Republicans, inspired by President Barack Obama’s recent drop in popularity, are newly optimistic about their chances of challenging him in 2012 and are focusing on some surprising names.

Some major donors and GOP strategists have approached Joe Scarborough, the host of MSNBC’s "Morning Joe,” about a national run, according to party sources.

Former Senate Majority Leader Bob Dole of Kansas, the Republican nominee in 1996, told POLITICO that he would like to see Army four-star Gen. David Petraeus — the head of the U.S. Central Command, which includes Iraq and Afghanistan — run for president as a latter-day Ike...