Newly elected Sen. Rand Paul (R-Ky.) said Sunday that he won't vote to raise the debt ceiling unless it comes with serious concessions from Democrats on the budget.

"I can't imagine voting to raise the debt ceiling unless we're going to change our ways in Washington," Paul said during an appearance on "Fox News Sunday." "I am proposing that we link to raising the debt ceiling — that we link a balanced budget rule, an ironclad rule that they can't evade."

Paul said attaching "token spending cuts" to the debt ceiling measure wouldn't be enough to win his vote.

"We have to change the rules and we have to say to Washington, 'balance the budget. You have to do it by law,' " Paul said. "And then I'll vote to raise the debt ceiling. But only if we have an ironclad balanced budget rule that we attach to the debt ceiling."

Paul also harkened back to then-Sen. Barack Obama's vote against raising the debt ceiling in 2006, calling the rhetoric now coming from the administration on the dangers of not raising the limit "disingenuous."

"They say either you raise it or the sky will fall and the end of the economy will happen," he said. "What about an in-between solution? What about we 'spend what we take in?' We bring in 200 billion dollars a month. Couldn't we just spend what we have instead of saying 'Oh, we have to shut down government?' "

Appearing alongside Paul, Sen. Chris Coons (D-Del.), who defeated Tea Party favorite Christine O'Donnell in November, said he too will push the Senate to make spending cuts and bring down the deficit. But Coons warned of consequences from playing "a political game of chicken with raising the debt ceiling."

On Thursday, Treasury Secretary Timothy Geithner fired a warning shot over the debt limit, writing to congressional leaders to warn of catastrophic results from a failure to raise the ceiling when it comes up for a vote in early spring.

The debt ceiling currently stands at $14.3 trillion, which could be reached as early as the end of March.