WASHINGTON — The White House is recruiting mayors, county commissioners and other local officials to promote and carry out President Obama's health care law in states like Florida and Texas, where governors are hostile to it. The effort comes as the administration is intensifying its campaign to publicize new health insurance options and to persuade consumers, especially healthy young people, to sign up for coverage when open enrollment starts on Oct. 1. To bring people into the insurance market, the White House is using techniques it used to mobilize voters during Mr. Obama's re-election campaign, with a particular focus on Hispanics, who are much more likely than other Americans to be uninsured.