(CNN) The Russia investigation and President Donald Trump's decision to fire FBI Director James Comey are sure to dominate the headlines out of Wednesday's Senate intelligence committee hearing, but that's not the reason that four top administration national security officials are appearing before the panel.

The officials are testifying because the committee leaders have to shepherd a bill through Congress before the end of the year to reauthorize a key National Security Agency surveillance tool that has been slammed by privacy advocates as ripe for abuse.

Wednesday's hearing is the committee's first step to make the case for re-authorization of Section 702 of the Foreign Intelligence Surveillance Act , which is the law the NSA uses to track emails and phone calls of non-US citizens -- while sometimes incidentally collecting communications of US citizens, too.

The administration officials -- Director of National Intelligence Dan Coats, acting FBI Director Andrew McCabe, NSA Director Adm. Mike Rogers and Deputy Attorney General Rod Rosenstein -- will testify that Section 702 is an essential national security tool to stop terrorism, a view most of the intelligence committee agreed with.

But their boss has made reauthorizing more complicated.

Trump's tweets alleging -- with no evidence -- that he was wiretapped by President Barack Obama , as well as his assertion that "unmasking" is the real Russia story, have thrown a wrench into the surveillance debate on Capitol Hill, raising concerns for some conservatives about whether the NSA's spying powers are being abused.

"We're not going to reauthorize these surveillance programs if the American people are not satisfied that their security is going to be safeguarded," Rep. Trey Gowdy, a South Carolina Republican and House intelligence committee member, said last month on Fox News.

House intelligence Chairman Devin Nunes' trip to the White House was about the alleged "unmasking" of Trump officials by former Obama national security adviser Susan Rice.

The communications of US citizens that the NSA collects in the process of tracking a foreign national are routinely "masked," where the identity of that citizen is hidden. But a handful of government officials have the authority to request that an identity be "unmasked" if it's relevant for national security purposes.

Last week, Nunes issued three subpoenas seeking details of "unmasking" of US residents by Rice, former CIA Director John Brennan and former US ambassador to the United Nations Samantha Power.

National security analysts and backers of the law argue that the unmaksing issue should remain separate from the debate over reauthorizing the NSA surveillance law.

"Section 702 should not become collateral damage in the unmasking debate," said Adam Klein of the Center for a New American Security.

Robert Chesney, a Texas University law professor and writer on the Lawfare national security website, said the unmasking controversy and Section 702 shouldn't be related, but now unmasking will "hang over" the renewal of the surveillance law.

"For whatever reason, they decided collectively to make as much stink as possible about unmasking in order to put the intelligence community on trial and change the narrative about Russia," Chesney said.

Privacy advocates argue changes are needed to the surveillance law to safeguard the communications of US citizens.

Last week, Facebook, Amazon, Google and other tech companies signed a letter to the House Judiciary Committee urging Congress to overhaul the surveillance law.

Andrew Crocker, a staff attorney at the Electronic Frontier Foundation, said one of the most significant reforms needed is to the so-called "backdoor search loophole," where intelligence agencies may conduct warrantless searches of US citizens' collected communications if the target of the surveillance was a foreign national.

Senators on the intelligence committee downplayed the role that Trump's tweets -- and broader views on unmasking -- would play in their efforts to reauthorize the law.

"There will be hurdles, but it won't have anything to do with the tweets," Florida Republican Sen. Marco Rubio told CNN.

"The President seems to complicate things from time to time, but it's hard for me to believe that FISA will not be renewed," said Sen. John McCain, an Arizona Republican.

Arkansas Sen. Tom Cotton and more than a dozen Republican senators, including Intelligence Chairman Richard Burr, introduced a bill Tuesday that would permanently authorize Section 702.

Democrats are more split than Republicans. Virginia Sen. Mark Warner, the top Democrat on the intelligence panel, supports renewing the NSA surveillance law, while Oregon Democrat Sen. Ron Wyden is one of the chief critics of the law in the Senate.

But both senators indicated Tuesday they plan to focus their questions on grilling Coats and Rosenstein over Trump's actions, saving the surveillance debate for another day before the law expires at the end of the year.

Burr said that even if Russia is likely to dictate Wednesday's hearing, he plans on sticking to the FISA script.

"I have no control of where hearings go, but I know that (Section) 702 re-authorization is an important issue, so that's where my focus is going to be and that's where everybody is programmed to talk about," Burr said.