(CNN) -

President Barack Obama battled with Sen. Rand Paul during their weekly addresses Saturday, with the latter describing it as "a war ... for the heart and soul of America."

Obama contrasted the views of Republicans and Democrats on Medicare, saying Republicans wanted to "turn Medicare into a voucher program" and "effectively end Medicare as we know it."

Paul, meanwhile, described the struggle as "a war between those who believe in the American Dream and those who cannot grasp what makes America great."

He portrayed his argument as one above politics -- saying "the enemy is not Barack Obama or the Democrats" -- yet went on to argue "the president has failed to lead."

"Even in an election year, I've offered to work with the president," Paul said. "I've called and written. I've ridden with the president on Air Force One and offered to help him build bridges, to repair our nation's infrastructure.

"But I've received no answer," he continued. "The president is missing in action. While America flounders, the president campaigns."

The enemy, Paul said, is a failure among Washington politicians to follow the Constitution, budgeting laws and Congressional rules. "The enemy is our lack of being bound by the restraints of the Constitution," he said.

Obama used his remarks to push back against Republican criticism that he has raided Medicare, as well as hit Republicans over their proposals for the program.

"As part of the Affordable Care Act, we gave seniors discounts on prescription drugs and made sure preventative care like mammograms are free without a co-pay," Obama said.

He argued his impact on the program includes "getting rid of wasteful spending in the health care system and reining in insurance companies -- reforms that won't touch your guaranteed Medicare benefits."

But, he continued, "Republicans in Congress have put forward a very different plan. They want to turn Medicare into a voucher program."

Obama charged that "one plan would force seniors to pay an extra $6,400 a year for the same benefits they get now."

But that number, which his campaign used in a recent television advertisement, refers to the first Medicare plan proposed by the Republican vice presidential candidate, who has since modified his plan. The independent fact checking website Politifact.com rated the claim made in Obama's TV ad as half true, considering that the plan was outdated but that Ryan's more recent proposal is not specific enough to be similarly evaluated.

Obama and Ryan, however, did find some common ground on the need to act urgently. Ryan said that the "Republic is under attack like no other time in our history," while Obama called for the parties to "strengthen and preserve [Medicare] for future generations."