The debate over reforming the National Security Agency is heating up in the Senate.

After what some see as a loss in the House, pro-reform lawmakers and advocates are hoping for a comeback in the upper chamber, where they are seeking an end to the NSA’s collection of bulk data from phone calls involving people in the United States.

“All the sides are talking and trying to figure out a solution that addresses concerns on all sides,” one person familiar with talks between stakeholders on the issue said.

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Advocates for reform thought they would win in the House after Patriot Act author Rep. James Sensenbrenner Jr. (R-Wis.) offered legislation to end bulk collection.

But in eleventh-hour negotiations between House leaders and the administration, reformers say the bill was watered down in a way that could allow bulk collection to continue.

Specifically, the final bill included an overly broad definition of “selectors,” the terms intelligence officials can use to search for information in large data sets, critics said.

In the Senate, reform advocates are talking to lawmakers about a more narrow definition, and there have been some signs of support for their position.

“I am interested in trying to find a clearer and more understandable definition and make clear that it prohibits bulk collection of information under these authorities,” Senate Intelligence Committee Chairwoman Dianne Feinstein Dianne Emiel FeinsteinMcConnell says Trump nominee to replace Ginsburg will get Senate vote Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence Intensifying natural disasters do little to move needle on climate efforts MORE (D-Calif.) said in her opening statement at a Thursday hearing on the issue.

The comments were notable from Feinstein, who has vocally defended the surveillance programs, since they first came to light last year. She asked officials from the intelligence agencies about further refining the definition of selectors, and Deputy Attorney General James Cole said his agency was open to it.

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“We’re more than happy to work with the committee … to try to put out language that really accomplishes what I think we all understand needs to be done,” he said.

“We’re trying to end bulk collection” without sacrificing national security, he continued.

Stephanie O’Sullivan, principal deputy director of national intelligence, echoed Cole’s comments.

“The Intelligence Committee understands and will adhere to the bill’s prohibitions of all bulk collection under these authorities,” she said.

Senate Judiciary Committee Chairman Patrick Leahy Patrick Joseph LeahyBattle over timing complicates Democratic shutdown strategy Hillicon Valley: Russia 'amplifying' concerns around mail-in voting to undermine election | Facebook and Twitter take steps to limit Trump remarks on voting | Facebook to block political ads ahead of election Top Democrats press Trump to sanction Russian individuals over 2020 election interference efforts MORE (D-Vt.), the lead Senate sponsor of the original USA Freedom Act, has repeatedly expressed disappointment in the House-passed version of the bill.

He has pledged to “fight for a stronger USA FREEDOM Act” that bans bulk data collection.

Other pro-reform committee members have joined Leahy’s calls.

Sen. Richard Blumenthal (D-Conn.) said he is “very hopeful” that Leahy will move ahead with his version of the USA Freedom Act.

Soon after the Snowden leaks started appearing last year, Blumenthal introduced a bill that would install a “constitutional advocate” at the Foreign Intelligence Surveillance Court to push back on government proposals for new surveillance programs.

While that measure was included in the original USA Freedom Act, it got changed as the bill moved to the House floor. The House-passed version of the bill creates a panel of experts that the court can consult as it rules on new surveillance programs.

“I am very hopeful that the Senate will act on a measure that is stronger in requiring a constitutional advocate and other measures that are more robust” than the House bill, Blumenthal said Thursday.

Sen. Al Franken Alan (Al) Stuart FrankenGOP Senate candidate says Trump, Republicans will surprise in Minnesota Peterson faces fight of his career in deep-red Minnesota district Getting tight — the psychology of cancel culture MORE (D-Minn.), who introduced his own surveillance reform bill last year, has also promised to push for more transparency.

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“I was disappointed that the transparency provisions in the bill the House passed, particularly the government reporting provisions, were basically gutted,” he said in a statement to The Hill.

At a minimum, he said any bill should include a requirement that the government “tell the American people roughly how many of them have had their information collected.”

Harley Geiger, senior counsel at the Center for Democracy and Technology, said these calls for stronger reforms from Senate Judiciary Committee members, including the Chairman, are “very encouraging.”

Geiger said he is “optimistic that they will make improvements to [the House-passed USA Freedom Act], but the precise nature of improvements is still being discussed.”