Washington (CNN) -- Herman Cain said Sunday some Americans would pay higher taxes under his "9-9-9" plan, but denied suggestions that the poorest Americans and middle-class would pay more.
"Some people will pay more. But most people will pay less," Cain said on NBC's "Meet the Press."
The former CEO of Godfather's Pizza has surged toward the head of the pack in the race for the Republican presidential nomination, with "9-9-9" a centerpiece of his economic platform.
The plan calls for doing away with almost all of the existing tax code and replacing it with a 9% flat federal individual income tax, a 9% flat federal corporate tax, and a new 9% national sales tax.
Some economists have raised serious questions about the plan, and several fellow Republican presidential hopefuls have attacked it, saying it would give the government a new revenue stream and not protect families from paying more.
On the NBC show, Cain was asked about an article in the Washington Post, which said the plan "would stick many poor and middle-class people with a hefty tax increase while cutting taxes for those at the top, tax analysts say."
Cain insisted the plan would get rid of the "invisible taxes that are built into everything we buy."
"For example, take a loaf of bread. The farmer pays taxes on his profits. The company that makes the flour, the baker, the delivery man. By the time that loaf of bread gets to the grocery store, there are a series of invisible taxes, which are also called embedded taxes. So in reality, those taxes go away, and so the price of goods don't go up," he insisted.
A check of the figures on CNN's "John King, USA" found a significant gap in revenue between Cain's plan, which would bring in $1.77 trillion in revenue, and the current tax structure, which brings in about $2.16 trillion.
Cain, on NBC, insisted that despite opposition in Congress, he believes he could push through such legislation as president. Ultimately, he argued, lawmakers will listen to their constituencies.
While some other candidates have found themselves at or near the front of the GOP pack and then quickly fallen behind, Cain insisted that won't happen to him because people are connecting with "the substance of my ideals."
Citing his positions on the economy and immigration as examples, he said, "That's why I don't think Herman Cain will be a flavor of the week," he said.
Cain recently rejected criticism by former Alaska Gov. Sarah Palin, who called him the "flavor of the week" after he won a much-watched Florida straw poll in September. Palin later announced she was not running for president.
A CNN poll of polls indicates that former Massachusetts Gov. Mitt Romney is on top of the GOP field of candidates at 23%, and Cain is just three points behind. Texas Gov. Rick Perry, who was a front-runner in the national polls from late August through much of September, trails Cain at 14%. The CNN poll of polls is an average of the latest four national surveys in the GOP race. It was compiled and released Thursday.
Polling in critical early voting states indicates that Cain is statistically tied with Romney in Iowa and South Carolina and that Cain has surged to second place behind Romney in New Hampshire.
On immigration, Cain said he supports enforcing borders with troops in some areas, promoting the path to citizenship that currently exists, and empowering "states to do what the federal government can't and won't do."
He said he opposes abortion rights, including in cases of rape or incest. But if the life of the mother could be at stake, "the family is going to have to make that decision."
When asked about his model for a Supreme Court justice, Cain cited Clarence Thomas. "I believe, despite attacks from the left, he basically rules and makes his decision in my opinion based on the constitution and solid legal thinking."
Cain also said race is "absolutely not" a factor in the race. He also explained that he prefers to identify as a "black American" rather than an "African-American."
"The roots of my heritage are in the United States of America," he said.
CNN's Martina Stewart contributed to this report.