The Senate did not take any action to extend or replace a controversial surveillance program set to expire at the end of the month. (C-SPAN)

Senators left Capitol Hill early Saturday morning without taking action to extend or replace a controversial surveillance program set to expire at month’s end, paralyzed by a debate over the proper balance between civil liberties and national security.

In an after-midnight vote, the Senate turned back a House-passed bill that would end the National Security Agency’s bulk collection of private telephone records, the only legislation that offered a smooth transition ahead of a June 1 deadline.

A small cadre of senators, led by Rand Paul (R-Ky.), then rejected a variety of short-term extensions to the current authority in a dramatic floor exchange. That led Majority Leader Mitch McConnell (R-Ky.) to recall senators to the Capitol a day earlier than planned, on May 31, for a rare Sunday session hours ahead of the deadline.

An Obama administration official said Saturday that because Senate did not take action, the process of winding down the surveillance program is now underway.

The rejection of the compromise legislation was the latest turn in a complex standoff over government surveillance authority that has pitted Democrats, House Republican leaders, Senate Republican leaders and Paul, a presidential candidate, against one another as members of Congress eyed a week-long holiday break.

It is unclear what difference a week will make. The positions of national security hawks like McConnell and civil libertarians like Paul have barely softened, while the House-passed, White House-supported compromise measure was unable to gain the 60 votes necessary to proceed. A procedural vote on the bill failed 57-42.

“Sometimes things change as deadlines approach,” Paul said as he left the Capitol early Saturday.

In floor remarks, he demanded simple-majority votes on two amendments to the House bill, known as the USA Freedom Act, in order to drop his opposition to moving it forward. “Our forefathers would be aghast,” he said about the spy program.

After McConnell ended debate, Paul tweeted, “The Senate will return one week from Sunday. With your help we can end illegal NSA spying once and for all.”

Sen. John Cornyn (R-Texas), McConnell’s top leadership deputy, said after the votes that “Sen. Paul is asking for something that nobody will agree to.” The amendments Paul is seeking, he said, would not comport with Senate rules.

“My hope is in the meantime ... after everybody gets a good night sleep and is thinking clearly, that we can figure a way forward on this,” Cornyn said.

Frustration with Paul — especially from fellow Republicans — became increasingly obvious as the long night wore on. Paul held the Senate floor for nearly 11 hours Wednesday to decry any extension of current law, and many had hoped that “performance,” as Sen. John McCain (R-Ariz.) called it, would suffice.

It did not. Paul objected to a 7-day extension to the current law, taking advantage of Senate rules protecting the right of an individual senator to oppose quick action on any question. McConnell then proposed, in turn, four-day and two-day extensions, which were opposed by Democrats Ron Wyden (Ore.) and Martin Heinrich (N.M.), respectively.

When McConnell finally offered a one-day extension, Paul objected again, prompting the unusual Sunday session.

“There’s a new breed in the Senate, and we have seen the manifestation of it,” McCain said.” One or two or three are willing to stand up against the will of the majority. Some time ago, the Senate people would sit down and try to work things out. And obviously these individuals don’t believe in that. But I’m sure it’s a great revenue raiser.”

Throughout recent days, Paul’s presidential campaign issued a steady stream of e-mail solicitations to supporters and a flurry of tweets to the world highlighting his efforts to end the NSA surveillance program.

Aside from Paul’s parliamentary maneuvers, intrigue surrounded whether the Senate’s action, when it comes, would gain House approval before the surveillance authority’s expiration.

The House, now on an extended recess of its own, passed the White House-backed bill replacing the existing program with one that would keep the phone records in private hands except under limited circumstances. But McConnell and most fellow Senate Republicans fiercely opposed that legislation, calling it untested and potentially harmful to national security.

In unusually lengthy floor remarks kicking off the Senate’s business Friday morning, McConnell said the system established under the House bill is “untried” and would be “slower and more cumbersome than the one that currently helps keep us safe.”

“At a moment of elevated threat, it would be a mistake to take from our intelligence community any of the valuable tools needed to build a complete picture of terrorist networks and their plans,” McConnell said. “The intelligence community needs these tools to protect Americans.”

Later in the day, White House press secretary Josh Earnest renewed calls to pass the USA Freedom Act, saying any other legislation would lead to a lapse in legal authority for the phone records program — which would phase out over a six-month period — as well as other less-controversial investigative tools.

“The fact is, we’ve got people in the United States Senate right now who are playing chicken with this,” he said, adding that “there is no plan B” if the House bill is not passed.

The controversy began in June 2013, when The Guardian newspaper published a document that revealed the National Security Agency was collecting “all call detail records” from Verizon. The document, leaked by former NSA contractor Edward Snowden, and the government’s subsequent acknowledgment of the program, touched off a national debate about the proper scale of U.S. surveillance.

In December that year, a presidentially appointed review group recommended that the government end NSA’s storage of phone data, citing “potential risks to public trust, personal privacy and civil liberty.” In January, 2014, President Obama called for an end to the agency’s bulk collection and essentially left it to Congress to come up with a replacement that would protect national security while respecting privacy.

A year ago, the House passed a version of the USA Freedom Act, but later that year the Senate failed by two votes to advance its own version — after McConnell led a filibuster to block it.

Senate Intelligence Committee Chairman Richard Burr (R-N.C.) on Thursday proposed extending the USA Freedom Act’s six-month transition away from bulk data collection to two years.

But Democrats and many House Republicans oppose any extension to the current legal authority, initially passed under Section 215 of the 2001 Patriot Act, or any substantive changes to the USA Freedom Act.

Rep. James F. Sensenbrenner Jr. ­(R-Wis.), a lead author of the USA Freedom Act, called Burr’s proposal a “last-ditch effort to kill” the House bill. “If the Senate coalesces around this approach, the result will be the expiration of important authorities needed to keep our country safe,” he said in a statement.

“[T]he Senate should make no mistake, if it does not pass the bill and the provisions expire — it will have a lot of questions to answer about why it decided to play legislative chicken with important intelligence tools,” said Rep. Adam B. Schiff (D-Calif.), ranking Democrat of the House Select Committee on Intelligence.

But Cornyn said Thursday he believed the other chamber would flinch: “The House isn’t going to let this go dark,” he said, exiting a lunchtime Republican caucus meeting Friday.

The Obama administration has spent days calling and briefing senators and reporters, arguing that the only path forward that avoids legal and operational uncertainty is to pass the USA Freedom Act.

Extending Section 215 as it is, they say, would be risky legally. This month, a federal appeals court in New York ruled that the NSA program was unlawful because it was not supported by that statute. It held off on halting the program only because it recognized that Congress was debating its future and might change the program or change the law to expressly authorize it.

Even a short-term reauthorization, administration officials say, would risk a federal court stopping the program — and there would be nothing at that point to replace it.

The American Civil Liberties Union, the plaintiff in the case heard by the appeals court, would likely seek an injunction if Congress passes a stopgap. “If this program is in place for any longer than June 1, our goal is to get a court order shutting the program down,” said ACLU staff attorney Alex Abdo.

Operationally, officials say, if it is not clear that they will have authority to continue running the program past June 1, they will have to begin dismantling it in the coming days lest they “run the risk of . . . continuing to collect without the authority” to do so, according to an administration official who spoke on the condition of anonymity.

McConnell has criticized the USA Freedom Act for not mandating that companies retain phone records for any period of time, thus risking that records that might prove important could be lost if they are not all collected upfront, as they are under the current program.

In fact, the NSA is collecting less than a full universe of all Americans’ call records, officials have acknowledged. The Washington Post reported last year that the collection is estimated at less than 30 percent given that, for technical reasons, at least two large wireless companies were not being collected from. That collection gap has not changed, sources said.

And as more and more companies offer fixed-rate plans, they have no need to keep records of individual phone calls for billing purposes, industry officials said.

The administration is also arguing that beyond the bulk records program, Section 215 is vital to the FBI in obtaining specific records of individuals in counterespionage and counterterrorism investigations. A second tool the bureau considers important is the “roving wiretap,” which allows the FBI to monitor suspected spies or terrorists who switch frequently from one phone to another. And a third tool allows authorities to surveil “lone wolf” suspects who are not tied to a particular terrorist group.

Director James B. Comey this week called them all “critical tools for the FBI that are going to sunset on June 1.”

Paul Kane contributed to this report.