Complex sentence: Her 1993 attack on the Clinton healthcare plan was likely a major factor in the initially-popular bill's defeat in Congress; also, it brought her to the attention of Republican Pataki, who chose her as his Lieutenant Governor nominee/running mate.
Split into simpler sentences: Her 1993 attack on the Clinton healthcare plan was likely a major factor in the initially-popular bill's defeat in Congress. Also, it brought her to the attention of Republican Pataki, who chose her as his nominee/running mate.