President Barack Obama criticized Republican rival Mitt Romney and running mate, Wisconsin Congressman Paul Ryan, telling thousands of people at two rallies Wednesday in eastern Iowa that he has protected Medicare, but the Republican ticket would turn it into a voucher system and end the program “as we know it.”

The argument over the health insurance program for seniors could be crucial, particularly in Iowa, a swing state with a large number of elderly.

It’s an issue both campaigns are eager to fight over.

Romney’s campaign is running a new television advertisement criticizing the president for $716 billion in cuts to Medicare. The cuts over 10 years will go toward paying for the new health care reform law and come from a variety of areas, including payments to hospitals and other health care providers and to private insurers who are part of the Medicare Advantage program.

The president’s campaign, meanwhile, released a new video that seeks to tie Romney to Ryan’s budget, which also assumes the same amount of Medicare cuts and the health care law’s repeal.

On the last day of a three-day bus trip across the state, Obama directly engaged on the issue in front of large, enthusiastic crowds in Dubuque and Davenport. He said his health care reform law provided seniors with savings on prescription drugs and that it would extend the solvency of the program, while not touching benefits.

“My plan’s already extended Medicare by nearly a decade,” the president said in Dubuque. “Their plan would end Medicare as we know it.”

The president also pointed to Congressional Budget Office estimates that say the Ryan plan would push more of the cost of health insurance onto seniors

Ryan’s plan would provide premium support payments to future retirees — only those who are now younger than 55 — to buy health insurance on the private market. He also would limit growth in the program’s costs.

“If it doesn’t keep up with costs, well, that’s the senior’s problem,” Obama warned in Davenport.

How much the president’s criticism on Medicare will stick to Romney remains to be seen.

Romney has said that it’s his budget, not Ryan’s, that the ticket is running on. And Wednesday morning, Romney said he will restore the $716 billion in Medicare cuts if he’s elected.

That would appear to distance Romney from a major part of Ryan’s budget plan, a key reason for the young congressman’s appeal among conservatives. It also could help to insulate Romney from the president’s criticism, however.

After the president’s remarks in Dubuque, the Romney campaign responded.

“President Obama has a long history of launching shameful political attacks on Medicare — but he’s the only person in the race who has actually cut Medicare,” said Ryan Williams, a spokesman. “President Obama cut $716 billion from Medicare to pay for Obamacare, and our nation’s seniors will pay the price with higher costs and fewer benefits.”

Republicans have defended Ryan’s plan by saying that it’s voluntary and that people could stay in traditional Medicare. But critics complain the change would no longer make it feasible to do so.

The president also mounted a defense of his health-care plan during both rallies, embracing the term “Obamacare,” which Republicans use as an epithet. As he’s said before, Obama said it fits, because “I do care.”

He said although Romney may be interested in repealing the health-care law, “the Supreme Court has spoken. It is the law of the land. We are moving forward.”

The president was joined by first lady Michelle Obama, who participated in the last leg of the Iowa trip. She drew big rounds of applause at both visits, as she described the president’s upbringing and his empathy for families that are struggling.

Both got a huge cheer as they mounted the stage at 11th and Christie streets in the Village of East Davenport.

The president, referring to the area as “the Quads” as he frequently does when he’s in the area, paid tribute to former U.S. Rep. Lane Evans from the Illinois Quad-Cities.

Then, he set out a series of issues in which he said Americans face a choice between him and Mitt Romney. They included taxes, the economy and energy.

Obama, whose 2008 caucus win here vaulted him to the presidency, has visited here frequently. And aides recapped the trip by saying the president and first lady have a special feeling about the state, and they felt the enthusiasm from supporters on the three-day trip, which began in Council Bluffs.

Polls say Obama and Romney are running fairly even in Iowa, and the Republican’s campaign mounted a vigorous effort at all of Obama’s stops to counter the president’s message.

In Dubuque and Davenport, former Republican Party of Iowa Chairman Matt Strawn and others echoed the Romney campaign’s Medicare argument, as he stood with sign-waving supporters outside Obama’s event. The Romney campaign also bought a full-page ad in the Quad-City Times on Wednesday in which a group of businesspeople criticized the president for his statements on the private sector.

That seemed to matter little to the crowd in the Village of East Davenport, which the Obama campaign estimated at 3,000.

The president and first lady got an enthusiastic response in a county that is likely itself to be closely contested over the last three months of the campaign. Obama won Scott County handily four years ago, but Republicans scored victories in the 2010 midterms and, historically, while voting Democratic over the past several presidential races, the county is usually more closely contested than it was in 2008.