(CNN) - Sen. Ted Cruz of Texas linked raising the debt ceiling to funding the Affordable Care Act in an exclusive interview Sunday on CNN's "State of the Union” with Candy Crowley.
“The debt ceiling historically has been among the best leverage that Congress has to rein in the executive," Cruz said.
He listed three objectives as Republicans approach the debt ceiling.
"No. 1, we should look for some significant structural plan and reduce government spending. No. 2, we should avoid new taxes, and No. 3, we should look for ways to mitigate the harms from Obamacare."
"Since 1978, we raised the debt ceiling 58 times," said Cruz. "Twenty times Congress attached very specific and stringent requirements, many of the most significant spending restraints. So the president's demand to jack up the nation's credit card with no limits, no constraints - it's not reasonable."
The United States will reach its borrowing limit on October 17.
The government temporarily shut down on October 1 after Republicans in the House held up the passage of a spending bill, which would allow the government to pay its bills, in an attempt to get changes or delayed implementation of the Affordable Care Act, President Obama's signature health care initiative.
Cruz is seen by some as the driving force behind the government shutdown, as he has urged fellow Republicans in the House to continue demanding that any plan to fund the government be tied to defunding the president's sweeping health care initiative.
Cruz said that letting Obamacare go further into effect "would destroy the private health care system." He blamed Senate Majority Leader Harry Reid for refusing to take up a series of piecemeal bills passed by the House to fund certain parts of the government. Democrats in the Senate and the White House say they will only pass a "clean" spending bill that does not carry restrictions or changes to the health care law.
The tea party favorite has been a target of blame from both Democrats and some Republicans for the shutdown standstill.
"The president and certainly Harry Reid and Senate Democrats have not been shy and using all sorts of inflammatory attacks," Cruz said about receiving criticism from Democrats and some within his own party.
"The fact that you're seeing those attacks, I think, is indicative of the fact that we're winning the argument. Obamacare isn't working."
According to a CBS News poll released this week, 72% of Americans disapprove of the shutdown, and more Americans blame congressional Republicans than blame Obama.
Despite this, Cruz doesn't think his actions have taken a negative toll on his party's image.
"Not remotely," Cruz said. "But I also think far too many people are worried about politics."