"It probably is not as big a deal as the president is making out," he said, noting that the FBI can use other tools, like warrants, in the interim.
"We're likely to be faced with only a few days where the FBI won't have a handful of tools that, frankly, they don't often use," said Clarke, who in 2013 recommended that the Obama administration end bulk metadata collection.
"I think terrorist elements have watched very carefully what has happened here in the United States," Brennan said on CBS's "Face the Nation" Sunday when asked whether terrorists would take advantage of a brief lapse. "They are looking for the seams to operate within, and this is something that we can't afford to do right now.
Three provisions of the PATRIOT Act -- including Section 215, which gives the NSA the authority to collect phone metadata -- are set to expire automatically at midnight tonight unless Congress works out a deal.
Two other provisions could also run out tonight: one that allows law enforcement to impose roving wiretaps on terror suspects who frequently switch phones, and another that allows officials to monitor suspected terrorists even if they can't establish a connection to a known terrorist organization. (This "lone wolf" provision has never been used.)
Though the House of Representatives passed the bill 303-121, it fell just three votes short of moving forward in the Senate.
In his weekly address, President Obama lauded the House for passing the measure, and encouraged the Senate to do the same.
If he's successful, "there is no plan B," according to the White House.
The NSA will begin shutting down its surveillance operation at 4 p.m. today, just as the Senate reconvenes. If it doesn't cancel the shutdown by 8 p.m., the stoppage becomes irreversible, and no data can be collected or analyzed until the system restarts, which could take an entire day.
"Heaven forbid, we've got a problem where we could have prevented a terrorist attack but we didn't do so simply because of inaction in the Senate," Obama said Friday.
ABC's Devin Dwyer and Jordyn Phelps contributed to this report.