Complex sentence: Because of his reputation for garnering support across party lines, it was rumored that he would seek the Republican nomination for Attorney General in 2006, but doing so would have opened his competitive, and probably Democrat-leaning, district to a threat from the Democrats.
Split into simpler sentences: Because of his reputation for garnering support across party lines, it was rumored that he would seek the Republican nomination for Attorney General in 2006. That would have opened his competitive, strongly probably Democrat-leaning, district to a threat from the Democrats.