DALLAS — It took him a while, but President Obama finally has a snappy comeback for Republican rivals who derisively refer to his 2009 health-care law as “Obamacare.”

“Folks go around saying ‘Obamacare.’ That’s right -- I care,” the president said at a fundraising luncheon in Dallas on Tuesday. He added of Republicans: “That’s their main agenda? That’s your plank? Is making sure 30 million people don’t have health insurance?”

The new catchphrase is part of Obama’s personality makeover as he more aggressively fights back against his political opponents. Health care is one of the major talking points for the GOP presidential candidates, who routinely pledge during debates and campaign appearances that they will roll back Obama’s health-care law.

Even former Massachusetts Gov. Mitt Romney, the GOP frontrunner who had championed a law in his state that provided similar health-care coverage, has said he would sign a presidential order to repeal the federal law on his first day in office.

“ObamaCare will lead to more spending, greater federal involvement in health care and negative effects on U.S. economic activity,” Romney wrote in a USA Today op-ed last spring.

On each leg of his nationwide tour to promote his Americans Jobs Act, Obama has tried out new lines to blunt his rivals’ criticisms. For example, when Republicans accused Obama of engaging in “class warfare” for proposing to raise taxes on higher-income Americans to pay for his jobs plan, Obama embraced the term.

“The Republicans in Congress call this class warfare,” the president said during a speech in Ohio last month. “Well you know what? If asking a billionaire to pay the same tax rate as plumber or teacher makes me a warrior for the middle class, I’ll wear that charge as a badge of honor.”

Obama and his aides have consistently defended the health-care law by stating that 1 million young people have health insurance because they are now allowed to remain on their parents’ insurance plans.

But Tuesday appears to mark the debut of the Obamacare quip. After it went over well in Dallas, he used it again in St. Louis during another fundraiser Tuesday night: “They call it Obamacare? I do care! You should care, too.”