Correction: An earlier version of the article misidentified the state in which retired Gen. Jerry Cannon is seeking the Democratic nomination for a House seat. Cannon is running in the 1st Congressional District of Michigan, not Minnesota. This version has been corrected.

Democrats are working hard to exploit massive unrest in the Republican Party over the looming government shutdown, which many see as one of their best chances of holding the Senate or even gaining the House in next year’s midterm elections.

White House officials and other Democrats have been content to watch in recent days as Republicans have torn into each other over strategic disputes and are in no rush to launch negotiations on how to avoid a shutdown.

Instead, they have attacked Republicans as reckless, pressuring them to decide whether to keep the government open with no strings attached — as Democrats favor — or shut it down.

The key to the Democratic strategy is a belief that a showdown is likely to play out similarly to the government shutdowns of 1995 and 1996, which turned public opinion sharply against the Republican majority.

“It wouldn’t be the worst thing for Democrats if [Republicans] tried to shut the government down,” Hillary Rodham Clinton, the former secretary of state and a potential 2016 presidential candidate, said in New York on Tuesday.

As Sen. Ted Cruz (R-Tex.) continues to deliver extended remarks on the Senate floor against Obamacare, here are the highlights in just three minutes. (Sarah Parnass/The Washington Post)

“We’ve seen that movie before, and it didn’t work out so well for those so-called obstructionists,” she added.

As a result, many Democrats welcomed Tuesday’s filibuster-style floor speech by conservative Sen. Ted Cruz (R-Tex.), who pledged to talk for as long as he could in an attempt to slow Democratic plans to advance a bill that would keep the government open while also funding President Obama’s signature health-care law. House Republicans voted to strip funding from Obamacare last week in exchange for keeping the government running.

The Cruz demonstration — which was opposed by many leading Senate Republicans and was set to end by Wednesday morning — plays into a Democratic strategy to try to ensure that the GOP is blamed for a shutdown if it occurs.

Congress must act by Monday night to avoid most agencies closing on Tuesday. The showdown is likely to serve as a launching point for a similarly contentious debate next month over raising the federal debt ceiling.

Looking ahead to the challenging midterm elections, Democrats see a potential political boon in the ongoing fights. Democratic candidates in some competitive races have begun to attack incumbent Republicans over the GOP effort to defund Obamacare, airing advertisements and targeting their offices with constituent calls.

“We’re going to make the case that 2014 is going to be a referendum between extremist Republicans and crisis and leaders with reasonable solutions,” said Rep. Steve Israel (D-N.Y.), chairman of the Democratic Congressional Campaign Committee. “It does create a narrow path for us.”

But Republican strategists say Democrats are overstating the potential benefits of the showdown for their side. They say that Democrats have their own problems — particularly support for Obamacare in the face of strong public opposition. Republicans have launched their own waves of television and Web ads linking Democrats in competitive districts to the health-care law.

“I don’t see how the debate thus far helps them in any way, shape or form,” said Daniel Scarpinato, a spokesman for the National Republican Congressional Committee. “It’s only highlighted how obsessed the Democrats are with protecting Obamacare, to the extent they will not agree with any compromises in order to stop or slow it down.”

But for Democrats, the experiences of 1995 and 1996, when government shutdowns breathed new life into Bill Clinton’s presidency, stand as a model.

“It didn’t go well for Republicans then, and there’s reason to believe that public opinion is more likely to be against them now,” said Jennifer Palmieri, White House communications director and a veteran of the Clinton White House.

Polls show that Americans agree with the Democratic view that Obamacare should remain law. Voters also strongly oppose a debt default or a government shutdown as part of a ploy to strip funding for the health-insurance expansion.

But despite Democrats’ convictions that they will come out ahead, there’s evidence that both sides may get blamed in a shutdown. One Pew Research Center poll this week reported that 39 percent of respondents would blame Republicans if the government shut down, compared with 36 percent who would blame Obama.

Another challenge for Democrats is that many Republicans are less vulnerable than they were in the 1990s because gerrymandering has narrowed the number of competitive seats in the House, with only about two dozen GOP seats in play.

“I’m not going to say the Democrats are going to pick up 20 seats because the 2010 redistricting redrew the districts in such a remarkable way,” said Democratic strategist Paul Begala.

As the conflict has escalated in recent weeks, the Democratic budget strategy has had two prongs: First, Obama and his party avoided negotiations with House Speaker John A. Boehner (R-Ohio) over changes to Obamacare or a deal over the debt limit, both of which are characterized by Democrats as not up for negotiation.

Second, Democrats have repeatedly targeted Boehner with attacks, portraying him as a weak leader who succumbed to tea party pressure to pursue the Obamacare defunding strategy.

The approach was evident when Obama called Boehner in recent days to warn him that he wouldn’t negotiate over either issue. Then, at the request of Senate Majority Leader Harry M. Reid (D-Nev.), Obama abandoned preliminary discussions to hold a bipartisan meeting with congressional leaders this week.

The congressional timeline is now such that Boehner will probably have to make a snap judgment about passing a funding bill on Monday or let large swaths of the government cease operations.

Publicly, the White House and Democrats have been working to make sure as much blame as possible is put on Boehner and the Republicans for a potential shutdown.

Senior Obama adviser Dan Pfeiffer wrote in a message to the White House e-mail list this week that “Republicans still care more about scoring political points on Obamacare than keeping the government open and our economy moving forward.”

Organizing for America, Obama’s former campaign organization, has attacked Boehner in television advertisements and other messages, and said it is planning rallies across the country as well.

The issue is already erupting in several competitive congressional contests.

In Illinois’ 13th District, for instance, Democratic candidate Ann Callis, a former judge, has attacked Rep. Rodney Davis (R) and other Republicans for putting “the livelihood of millions of Americans in doubt to prove a political point.”

In Michigan’s 1st District, retired Gen. Jerry Cannon warned after Republicans voted to strip funding for Obama’s health-care law that “the paychecks of troops and other military workers would be delayed indefinitely” if the government shut down.

Republicans, meanwhile, are targeting Democratic incumbents with ads linking them to Obamacare. The National Republican Congressional Committee has attacked Rep. John Barrow (D-Ga.), warning of “higher premiums for Georgia families.”

GOP television ads have also accused Rep. Patrick Murphy (D-Fla.) of “voting to keep the scandal-ridden IRS in charge of enforcing Obamacare.”

Philip Rucker contributed to this report.