WASHINGTON -- The Senate's top Democrat is raising the possibility his party may try to stall President Trump's FBI nominee until his administration agrees to have a special prosecutor investigate Russia's meddling in the 2016 election and possible ties to the Trump campaign.

FULL COVERAGE: The firing of James Comey

The threat from Sen. Chuck Schumer, D-New York, is more fallout from Trump's firing last week of FBI Director James Comey and the evolving reasons for the dismissal.

Democrats would need Republican support to follow through because it takes 51 votes for confirmation -- and Republicans now hold 52 seats.

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Schumer said on CNN's "State of the Union" that "the key here, of course, is getting some of our Republican colleagues to join us. We're hoping. We're waiting."

Trump told reporters aboard Air Force One on Saturday that he may select Comey's successor before leaving for his first foreign trip next week.

"We can make a fast decision," Mr. Trump said. "These are outstanding people that are very well known, highest level. So we can make a fast decision."

Department of Justice officials spent the day Saturday interviewing candidates for the permanent FBI director role, including McCabe, Republican Sen. John Cornyn of Texas, attorney Alice Fisher, federal Judge Henry Hudson and former Homeland Security Adviser Fran Townsend, who is also a CBS News national security analyst.

Late in the day, Mike Rogers, a former congressman, was a last-minute addition to the list of interviewees. Rogers was endorsed for the permanent director role earlier Saturday by the FBI Agents Association, which represents 13,000 current and former agents.

The DOJ also says several current FBI and intelligence officials were being interviewed for the interim position, including Special Agent in Charge Adam Lee, who returned to DOJ for a second interview Saturday. Earlier in the week, DOJ officials said they were close to naming an interim director, but have yet to do so.

Rep. Adam Schiff, D-California, said on "Face the Nation" Sunday that he is urging the Trump White House to "pick someone who is completely apolitical, who doesn't come out of the political process" to lead the bureau and to help "give credibility to the Russia investigation that right now is severely in jeopardy."

"One of the, I think, heightened responsibilities we're going to have in the House Intelligence Committee is making sure that, whoever comes in, this investigation by the bureau goes on unimpeded, because the FBI has a reach that neither our committee nor the Senate committee has," Schiff added.