GOP health care act sponsor to a Republican opponent: The bill will 'save a lot of money'

— -- Sen. Lindsey Graham, R-S.C., directly addressed fellow Republican Sen. Rand Paul of Kentucky over his opposition to the latest GOP bill aiming to repeal and replace Obamacare, saying the new legislation would "save a lot of money."

"Rand Paul objects to the taxes, but when you look at the bill, Rand, we save a lot of money over time for Medicaid," Graham said in an interview with ABC News Chief Global Affairs Correspondent Martha Raddatz on "This Week" Sunday. “We've put a cap on Obamacare growth to make it more sustainable, more affordable, more flexible.”

Graham and fellow GOP Sen. Bill Cassidy of Louisiana both appeared on the show to talk about their legislation, the Graham-Cassidy health care bill.

Despite the announced opposition of Paul and Republican Sen. John McCain of Arizona as well as all Senate Democrats, Graham said he is optimistic that Republicans will be able to pass the bill.

"We're moving forward and we'll see what happens next week. I'm very excited about it. We finally found an alternative to Obamacare that makes sense," Graham said.

“I think we're going to get the votes next week,” Graham added. “And the fight goes on. It is a fight worth having.”

McCain announced his opposition to the legislation in a statement Friday, saying he cannot in “good conscience vote for the Graham-Cassidy” bill.

Sen. Susan Collins of Maine has expressed reservations about the bill but said she wants to wait for the Congressional Budget Office to release its analysis before she makes her final decision.

The Graham-Cassidy proposal has also been met with criticism from organizations representing the country's doctors, hospitals, and health insurers.

"While we sometimes disagree on important issues in health care, we are in total agreement that Americans deserve a stable health care market that provides access to high-quality care and affordable coverage for all. The Graham-Cassidy-Heller-Johnson bill does not move us closer to that goal. The Senate should reject it," said a joint letter released Saturday by the American Medical Association, American Academy of Family Physicians, American Hospital Association, Federation of American Hospitals, America’s Health Insurance Plans, and BlueCross BlueShield

When asked about the letter on "This Week," Graham dismissed the organizations' concerns and said their criticism doesn't surprise him.

"The fact that insurance companies are objecting to the fact they no longer get direct payments from the federal government, the same amount of money goes to states to set up new health care systems that won't fail, doesn't surprise me," he said.

"I would have been surprised if these people were for our bill, because we take money away from them, we give it to state governments to design systems that will deliver a better outcome," Graham said.