TAMPA, Fla. -- Sen. Rand Paul (R-Ky.), on the eve of his address to the Republican National Convention, lived up to his maverick reputation, calling out the budget put forward by Mitt Romney's running mate, Rep. Paul Ryan (R-Wis.).

"It's too tepid," Paul told HuffPost, pointing out that Ryan's plan does not balance the budget for 28 years.

Paul is the son of Rep. Ron Paul (R-Texas), Romney's former rival for the GOP presidential nomination. Ron Paul's supporters in the Maine delegation walked out of the RNC in protest Tuesday evening over a credentials fight, and chanted the elder Paul's name during the roll call vote to nominate Romney. The younger Paul has criticized the budget of Romney's vice presidential pick before, and on the same grounds.

But he did not hold back his criticism Tuesday evening, even though he is scheduled to speak Wednesday -- the same night as Ryan, who will deliver the prime-time address to the convention delegates one night before Romney accepts the Republican nomination.

And with his comments, Paul signaled a willingness to buck the party establishment, to a degree. He has already angered many of his father's supporters by endorsing Romney in the first place. It is a delicate balancing act for a first-term senator who -- now that the elder Paul is retiring from Congress -- could inherit a genuine grassroots movement, but has worked hard to build bridges within the GOP establishment that many in the "Liberty Movement" detest.

Paul lumped in Ryan, and his budget, with a portion of the GOP that he says is not dealing boldly enough with the nearly $16 trillion national debt and increasingly burdened entitlement program budgets. That's quite a contrast to many in the Republican Party and the conservative movement who have welcomed Romney's choice of Ryan as a bold decision to take on big problems with big solutions.

"The number one problem we face in the country is the debt. It's overwhelming us as a country and it will overwhelm us," Paul said. "Republicans understand that in a general sense. But their response to it is often tepid, waiting 28 years to balance the budget, when the left wing is just going crazy over the Ryan budget, saying, 'Oh my God, it's so extreme.'"

Ryan, when he released his proposal, said that he believed it could balance the budget "in the mid-to-early 2020s ... much sooner than [Congressional Budget Office's] estimated balance date of 2039."

"It doesn't balance for 28 years," Paul said. "Many Republicans are for a balanced budget amendment. It says you have to balance in five years."

As to his relationship with his father's supporters, Paul said it is "presumptuous of anybody to say, 'Well I'm going to be the leader of the Ron Paul people.'"

"Ron Paul generated the movement and we'll see where it goes from here," he said.

Ron Paul gave what was labeled as "a swan song" speech to supporters here in Tampa on Sunday evening. But Rand said he was not wistful or sentimental as he watched the 77-year-old obstetrician speak.

"I don't see him going away really. I think he's going to continue to travel around the country. He loves talking to college crowds. I think he'll continue to do that," he said.

Paul said he is fairly confident that the Paul movement, by and large, still does support him despite decisions like the one to endorse Romney.

"I introduced my dad [on Sunday] and I would say 98 percent of them were enthusiastic about me being there," he said. "We had a book signing and hundreds of people came and bought the book. I spent two hours signing books."

"So we think that the crowd likes me but I don't presume to say these are all my people and it's automatically me that's going to lead them. I don't think it's that simple."

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