Both Ryan and President Obama addressed the American Association of Retired Persons gathering.
Ryan quoted President Lyndon Johnson's remarks when he signed the Medicare bill. Johnson said the guarantee of health coverage for those over 65 helped both young and old.
"Today, our nation faces a political turning point. Government mismanagement and political cowardice are threatening both sides of LBJ's pledge," Ryan said. "Seniors are threatened by Obamacare, a law that would force deep cuts to real benefits in real time for real people."
"The first step to a stronger Medicare is to repeal Obamacare because it represents the worst of both worlds," he added.
Ryan didn't mention that his own plan for Medicare includes the same cuts Obama's health plan does.
Ryan, a congressman from Wisconsin, and Obama, who spoke from Washington via a video hookup, used older relatives as examples.
Ryan's 78-year-old mother joined him in New Orleans while Obama paid tribute to his "fiercely independent" grandmother, Madelyn Dunham, who died in 2008 two days before he was elected president.
"I have strengthened Medicare as president," Obama said. "We've added years to the life of the program by getting rid of taxpayer subsidies to insurance companies that weren't making people healthier. And we used those savings to lower prescription drug costs and to offer seniors on Medicare new preventive services like cancer screenings and wellness services."