Sen. Chuck Schumer, D-N.Y., accused Republicans of "putting their heads in the sand."
"Mueller's testimony was a clarion call for election security," Schumer said. "Mueller's testimony should be a wake-up call to every American, Democrat, Republican, Liberal, Conservative, that the integrity of our elections is at stake."
Mueller told House members Wednesday, at a high-profile hearing delving into the special counsel's investigation of Russian interference in the 2016 election that the Putin-led government is still at it.
"It wasn't a single attempt. They are doing it as we sit here, and they expect to do it in the next campaign," Mueller said Wednesday.
When asked about this warning, Sen. Chuck Grassley, R-Iowa, agreed but he signaled that the federal government had success in stopping foreign interference in 2018.
"There's something I can hint at, but I can't go into specifics. There is interference going on, and a lot of it was going on before the 2018 election," Grassley said, referencing information gleaned from a closed-door briefing. "But what I can't tell you -- because it was a secured briefing -- is there was a lot of success stopping it."
But McConnell said Democrats were just trying to make political hay on the heels of the Mueller testimony in their attempt to bring up a House bill that would mandate the use of paper ballots in states' election systems and provide additional funding to the federal, nonpartisan Election Assistance Commission.
"This is partisan legislation from the Democratic House of Representatives," McConnell said, noting that the bill garnered just one GOP vote in that chamber and was designed to give Democrats the political upper-hand.
"It's very important that we maintain the integrity and security of our elections in our country," the GOP leader said, but he added, "any Washington involvement in that task needs to be undertaken with extreme care, extreme care and on a thoroughly bipartisan basis. Obviously this legislation is not that. It's just a highly partisan bill from the same folks who spent two years hyping up a conspiracy theory about President Trump and Russia."
But the Kentucky Republican, who is running for a fifth term in 2020, has shut down nearly every effort to bring election security to the Senate floor.
Many of the bills Democrats have sought to call up this week -- and in previous weeks -- are bipartisan.
The DETER Act, for instance, co-authored by Graham and Sen. Dick Durbin, D-Ill., would allow federal officials to deport anyone involved in election interference and refuse admittance to the country anyone found guilty of such acts.
Grassley told reporters Thursday that he wants to see that bill, for which he voted, considered by the Senate. He also added that he would favor the House bill Schumer tried to pass on Thursday if "you took out things in it that federalize state elections."
The Judiciary Committee also passed legislation to make it a federal crime to hack into a state voting system. That legislation passed the Senate earlier this month and awaits House consideration.
But McConnell has stopped other attempts to legislate around the issue.
Sen. Jim Lankford, R-Okla., a lead sponsor of an election security bill with Sen. Amy Klobuchar, D-Minn., echoed the concern of many Republicans that elections remain under state control, but said he wants to see his bill passed soon, though final tweaks are being made.
The Lankford-Klobuchar bill would provide security clearances for state election officials, state-to-state cooperation regarding potential interference and encourage states to have auditable voting systems.
But Lankford made clear that there is no time to get updated election equipment into states by the 2020 election.
"I've had folks say, 'We need to hurry to get money out the door to the states so they can buy new systems, but that's just not going to happen," Lankford said, noting that there is no way to install equipment and test it in time for 2020 primaries. "It's really 2022 that we're talking about here."
Lankford did say that -- after regular briefings with the Department of Homeland Security -- he is confident in the security of the 2020 elections.
Missouri Sen. Roy Blunt, chairman of the Rules Committee -- which has oversight of elections -- agreed and said federal legislation is not needed.
"When you talk to anyone responsible for elections or for monitoring outside intervention and ask them, 'do you need any legislation you don't have,' whether that's the FBI or NSA or Homeland Security, the answer is always 'no, we don't need more legislation,'" Blunt said, adding, "And I think it's fair to say Congress is paying attention to that."
And though states have indicated that they need more money to upgrade election systems, Blunt said there are still federal dollars allocated but unspent.
"There's $382 million that's not been spent by the states yet," the chairman said.
While some Republicans feel no further action is needed, the bipartisan Senate Intelligence Committee on Thursday issued a long-awaited bipartisan election security report in which both the chairman, Sen. Richard Burr, R-N.C., and vice chairman, Sen. Mark Warner, D-Va., said more needs to be done.
"There is still much work that remains to be done, however," Burr said, while touting the work federal and state officials are now doing together to harden the nation's election infrastructure.
"Our bipartisan investigation identified multiple problems and information gaps that hindered our ability to effectively respond and defend against the Russian attack in 2016," Warner said, "Since then -- and in large part as a result of the bipartisan work done on this issue in our Committee -- the intelligence community, DHS, the FBI and the states have taken steps to ensure that our elections are far more secure today than they were in 2016. But there's still much more we can and must do to protect our elections."
The report warns, "Despite increased focus over the last three years, some of these vulnerabilities, including aging voting equipment, remain. As states look to replace machines that are now out of date, they should purchase more secure voting machines. At a minimum, any machine purchased going forward should have a voter-verified paper trail."
Sen Richard Blumenthal, D-Conn., joined Schumer on Thursday, and attempted to call up legislation that would mandate that any campaign official report to the FBI any foreign interference or attempted interference.
"The issue of election security goes to the core of national security. In the last national election, this nation was attacked. It was as pernicious and as invidious as any on our history," Blumenthal said.
But McConnell objected.
"This is all about the faith in this country," Schumer warned. "If we lose faith in our electoral process, democracy begins to walk away from us, and we'll be a different country."