House Democrats have a message for GOP leaders eager to move beyond the Russia controversy following the resignation of national security adviser Michael Flynn: Not so fast.

"This is not the end, this is just the beginning," Rep. Joseph Crowley (N.Y.), chairman of the House Democratic Caucus, told reporters in the Capitol Tuesday. "This is larger than Flynn."

The comments set the stage for a messaging war on Capitol Hill between Republican leaders, who are hoping to move beyond questions of the White House's ties to the Kremlin, and Democrats, who are amplifying their calls for a deeper dive in the wake of Flynn's resignation.

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Flynn stepped down from his post atop the National Security Council late Monday night, following revelations that he had misled top White House officials — including Vice President Pence — about the nature of a pre-inauguration discussion he'd had with the Russian embassy.

Flynn had initially told Pence the conversation did not broach the topic of U.S. sanctions on Russia, which led the vice president to defend Flynn in a series of subsequent media interviews. After The Washington Post reported last week that Flynn had, in fact, discussed sanctions, Pence was reportedly furious.

Flynn stepped down after less than a month on the job, and many Republicans are eager to put the controversy to bed.

GOP leaders — including Speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (Wis.), House Oversight Chairman Jason Chaffetz Jason ChaffetzThe myth of the conservative bestseller Elijah Cummings, Democratic chairman and powerful Trump critic, dies at 68 House Oversight panel demands DeVos turn over personal email records MORE (Utah) and House Intelligence Chairman Devin Nunes (Calif.) — said Tuesday that they have no plans to dig deeper into Flynn's connections to Russia. Their focus, Ryan said, is repealing ObamaCare.

But Democrats are dubious that Flynn acted on his own, and they're pressing for a bipartisan probe to uncover any potential conflicts of interest between the White House and the Russians.

"It defies reason," said Rep. Peter Welch Peter Francis WelchShakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' Vermont Rep. Peter Welch easily wins primary Vermont has a chance to show how bipartisanship can tackle systemic racism MORE (D-Vt.). "People in that position don't do things without authorization."

The House and Senate Intelligence committees are both looking into Russia's interference in last November's elections, but those deliberations are being largely performed outside the public eye.

Crowley said the controversy swirling around Flynn only heightens the need for a broader probe of potential Russian influence in full daylight.

"The real question with respect to Flynn is: What did President Trump know, and when did he know it?" he asked.

"Did the president order Flynn to call the Russians? Did he seriously not know that his campaign adviser was calling Russians? What does President Trump have to hide?"

The minority Democrats have no power to launch an investigation on their own, a situation they readily acknowledge.

"We can't force them to do it, you're absolutely right," said Rep. Linda Sánchez (D-Calif.), vice chairwoman of the caucus. "But the people of the United States of America can. They just need to ratchet up the pressure."

Sánchez also took a shot at the GOP leaders who are ready to move on to other issues.

"Speaker Ryan, Jason Chaffetz, Devin Nunes, where is your spine?" she asked. "Do you care about our national security, because if you do, you cannot sweep this under the rug."