Washington (CNN) Sen. Rand Paul is not backing down on his pledge to end major provisions of the Patriot Act, warning on Saturday that he will keep up his fight as the Senate readies for a rare Sunday session.

"There has to be another way," the Kentucky Republican tweeted. "We must find it together. So tomorrow, I will force the expiration of the NSA illegal spy program."

I am ready and willing to start the debate on how we fight terrorism without giving up our liberty.

The National Security Agency's authorities -- which, among other powers, allow the agency to collect telephone data on millions of Americans and store that data for five years -- will end at midnight Sunday unless the Senate approves an extension.

Last week, Republicans were unable to find 60 votes to break a filibuster on either an extension of the existing law or a House-passed bill, the USA Freedom Act, that would have telecommunications companies hold the data and require the government to get a warrant to access it.

Paul and his allies are limited in their ability to derail the legislation altogether. But their opposition to any bill authorizing the programs would mean the Senate would be stuck in many hours of debate -- perhaps lasting days -- before anything could be passed by majority vote because of complex Senate procedural rules. By then, the authorities would have lapsed and the government would need time to get them back online.

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In a statement, Paul explained why he was taking a stand in the Senate.

"The callous use of general warrants and the disregard for the Bill of Rights must end. Forcing us to choose between our rights and our safety is a false choice and we are better than that as a nation and as a people," he said.

Paul also acknowledged in his statement that there is a need for a "robust intelligence agency" to defend against terrorism, but added, "We do not need to give up who we are in order to defeat them."

If there is no agreement by Sunday, not only would the government need to stop its bulk collection of phone data, but also authorities would not be able to conduct surveillance of so-called "lone wolf" terrorists who are not American citizens and not believed to be part of an identified terrorist group. The government would also lose its ability to conduct "roving wiretaps," a program that gives the government the ability to track various phones used by the same person.

On Friday, President Obama warned that without the data collection and surveillance programs, a terrorist could slip past U.S. intelligence.

"Heaven forbid we've got a problem where we could have prevented a terrorist attack or apprehended someone who is engaged in dangerous activity, but we didn't do so simply because of inaction in the Senate," Obama said in the Oval Office.

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"When it comes to foreign policy, which is an increasingly important issue, his statements yesterday and some of his previous statements I just think render him unsuitable," Louisiana Republican Gov. Bobby Jindal told CNN's Wolf Blitzer on Friday.

A spokesman for Senate Minority Leader Harry Reid used Paul's intransigence to hit Senate Majority Leader -- and fellow Kentucky senator -- Mitch McConnell, saying Saturday that "if McConnell cannot convince the man he endorsed for president to back off (a) filibuster, he has no one to blame but himself."

Paul said Saturday he is not doing this to "obstruct," but rather that he wants to start a debate on how to better fight terrorism, saying "sometimes when the problem is big enough, you just have to start over."

But Paul has used his strident opposition to some of the government surveillance efforts to raise his profile and to raise money for his presidential campaign, including selling T-shirts this week that read, "the NSA knows I bought this Rand Paul T-shirt."