The Virginia senator -- a former governor and Democratic National Committee chairman -- is among the Democrats reportedly on Hillary Clinton's short list of potential running mates.
The biggest criticism is that, compared to options like Massachusetts Sen. Elizabeth Warren, who could excite liberals, or Housing and Urban Development Secretary Julian Castro or California Rep. Xavier Becerra, who could attract Latino voters, Kaine -- who is fluent in Spanish himself -- is boring.
Asked on NBC's "Meet the Press" Sunday about those characterizations, Kaine didn't disagree.
"But boring is the fastest-growing demographic in this country," he said.
Kaine and Labor Secretary Tom Perez, two Democrats often discussed as vice presidential options for Clinton, both appeared on Sunday news shows.
On ABC's "This Week," Perez wouldn't directly answer questions about his interest in the role.
"I want to make sure that Hillary Clinton is the next president of the United States, because we need Secretary Clinton's focus on making sure that we build an America where our values of inclusion and opportunity for everyone are the values that bring us together," he said. "And so that's why it's been a real privilege to work for this president who I think is one of the most consequential presidents in American history, and it's a real privilege in my personal capacity to help Secretary Clinton."
Kaine, an early Clinton endorser, noted on "Meet the Press" that he encouraged the former secretary of state to run for president in May 2014.
"I decided that by reason of character, by reason of background and experience, but especially by reason of results, she would be the most qualified person," he said.
Kaine, who is Catholic, was also pressed on his stance on abortion.
"I would say, people use labels all the time, but I'm kind of a traditional Catholic: Personally, I'm opposed to abortion, and personally, I'm opposed to the death penalty," he said.
But, he said, he opposes abortion restrictions as a matter of public policy.
"I deeply believe -- and not just as a matter of politics, but even as a matter of morality -- that matters about reproduction and intimacy and relationships and contraception are in the personal realm. They're moral decisions for individuals to make for themselves. And the last thing we need is government intruding into those personal decisions," Kaine said.
"So I've taken a position which is quite common among Catholics -- I got a personal feeling about abortion, but the right role for government is to let women make their own decisions," he said.