(CNN) Senate Majority Leader Mitch McConnell is refusing to buckle to the near constant drumbeat from Democrats -- and some Republicans -- about the need to pass election security legislation in the wake of the report from special counsel Robert Mueller that found Russia interfered in the 2016 election .

The Kentucky Republican, who believes strongly that elections should be primarily controlled by state and local authorities and not managed by Washington, argues that the federal government has already responded to the problems raised from the 2016 campaign and more does not need to be done at this time.

McConnell thinks Democrats have poisoned the water through their early legislative efforts on election security.

Still, moving forward with some of the bills pushed by Democrats -- namely to require FBI disclosure for any foreign assistance -- would amount to an implicit rebuke of Trump, a fight that Republican leaders are eager to avoid.

Behind the scenes, congressional Democrats are finalizing their plans to mount a pressure campaign on McConnell in the weeks ahead to try to shame him for his opposition to these matters.

House Democrats are planning to pass a package of bills this summer aimed at shoring up the nation's election systems, including requiring FBI disclosure of offers for foreign assistance, something the Trump campaign didn't do in 2016 after Trump's eldest son was offered Russian dirt on the Clinton campaign . And Senate Democrats plan to return again and again to the floor to seek unanimous consent to pass election security bills, like the one they offered Thursday, which was blocked by Republicans that would have required any campaign that is offered assistance from a foreign government to report that to the FBI.

Democrats also see the upcoming appropriations process as a place the can use their leverage to boost spending for election security.

In a high-profile speech last month after the Mueller report was issued, when McConnell declared "case closed" against President Donald Trump, the GOP leader spelled out the steps the Trump administration and the GOP-led Congress took during the last session to respond to the foreign interference. He argued progress was made because there was not a repeat of the 2016 problems during the 2018 midterm elections.

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"With respect to election security: Congress appropriated hundreds of millions of dollars to state governments to shore up their systems," McConnell said. "The administration increased information-sharing from the Department of Homeland Security in cooperation with the states. And according to press reports, the Department of Defense has expanded its capabilities and authorities to thwart cyber threats to our democracy. No longer will we just hope Moscow respects our sovereignty; we will defend it. These are just a few examples. There's already evidence they're having an effect."

He added, "We just had the 2018 midterm elections. Thanks to this administration's leadership, all 50 states and more than 1,400 local election jurisdictions focused on election security like never before. DHS provided resources to localities for better cybersecurity and private social media companies monitored their own platforms for foreign interference. Thanks to efforts across the federal government, in 2018, we were ready. That clearly is progress."

This week, Senate Minority Leader Chuck Schumer rejected McConnell's reasoning and implored him to pass legislation.

"Why isn't he moving bills onto the floor -- bipartisan bills to deal with election security in 2020. FBI Director (Christopher) Wray said it's going to be worse in 2020 than it was in 2016. And because the Russians laid off in 2018, a non-presidential year, doesn't mean we can sit and do nothing .And yet that seems to be what McConnell wants to do," Schumer said.

On Fox News Thursday night, McConnell reiterated that the 2018 cycle was not interfered with like the 2016 campaign was and that he would resist Democratic efforts to "nationalize everything."

"This administration did a terrific job of working with state and local officials to make sure we had an honest election in 2018 with minimal to no interference. Where is the applause for that?" he asked. "I'm open to considering legislation but it has to be directed in a way that doesn't undermine state and local elections. The Democrats would like to nationalize everything. They want the federal government to take over the election process because they think that would somehow benefit them."

In the House

Democrats on the House Administration Committee may release bill text of a new proposal as soon as next week, according to aides. The exact contents of the proposal are still being hammered out. But it could include provisions to mandate states and localities maintain paper ballots, as well as to prohibit campaigns from soliciting or accepting foreign assistance.

The chairman of the committee, Rep. Zoe Lofgren, a Democrat of California, may take up the plan in the coming weeks in the hopes of pushing the plan through the full House before the August recess.

There are several other bills being pushed through the House, which could be wrapped up in the larger package. Among the bills is one pushed by Rep. John Sarbanes, a Maryland Democrat. House Speaker Nancy Pelosi touted legislation by the congressman at her weekly news conference on Thursday, describing it as "closing foreign money loopholes."

A separate bill, offered by Rep. Tom Malinowski, a New Jersey Democrat, called the Anti-Collusion Act, would require campaigns to report to the Justice Department any assistance offers from a foreign power or a domestic entity that involves illegal activity.

Pelosi touted House Democratic efforts on election security on Thursday, saying that Democrats have "a package that we're putting together in light of the Mueller report."

"We have a package that we're putting forth in light of the Mueller report, a package of legislation, duty to report if someone comes to you, mandating that campaigns report foreign offers of assistance," she said.

Pelosi added, "It's so self-evident as a matter of ethics, but we'll have to codify it, mandating a duty to report for campaigns reporting foreign interventions in our elections."

Democrats on the staff level are calling the effort a campaign to "end crime, corruption and coverups," but it's unclear if the Democratic leadership will use that as its central message when the package comes to the floor.

In the Senate

One of the most prominent bills under consideration in the Senate was originally co-authored by Oklahoma Republican Sen. James Lankford and Minnesota Sen. Amy Klobuchar, who is running for the Democratic nomination for president. According to Lankford's staff the bill, which has not been finalized or introduced, "streamlines cybersecurity information-sharing between federal intelligence entities and state election agencies; Expedites security clearances to state election officials; Provides support for state election cybersecurity infrastructure and operations; and, Ensures the auditability of state's elections."

Despite repeated requests to McConnell's aides to explain the leader's opposition to the bill, they declined.

At a hearing of the Senate Rules Committee last month, Sen. Dick Durbin of Illinois, the second-ranking Democrat, pressed Chairman Roy Blunt, a Republican of Missouri, why he wouldn't let the committee vote out the legislation.

Blunt suggested in response that McConnell wouldn't be willing to put in on the floor because he is worried about it going to conference committee and possibly merged with a far-reaching voting and government ethics overhaul offered by House Democrats called HR 1.

"I think the majority leader just is of the view that this debate reaches no conclusion and frankly I think the extreme nature of ... HR 1 from the House even makes it less likely that we're going to have that debate," Blunt said at the time.

McConnell has railed against HR 1 since it was introduced, arguing it was designed to keep Democrats in office.

While Democrats haven't able to persuade McConnell to take up legislation, they did get him to agree to hold a briefing for all-senators on the state of election security. McConnell announced this week that briefing will take place soon but didn't say when.