But more significant, as they prepare for an election in which they plan to run on income inequality and improving the middle class, the more times Republicans vote against an extension of popular benefits for unemployed individuals, or the House refuses to take up the issue, the better.

The Democratic Congressional Campaign Committee on Wednesday blasted out a CBS News polls showing that 65 percent of Americans—and, importantly, an equal number of independents—support extending unemployment insurance benefits.

With Republicans voting against the issue or avoiding it altogether, while simultaneously "spending a full day debating new restrictions to women's health," one national Democratic operative said, that fits in well with the party's broader electoral message.

National Democratic strategists are already messaging on the unemployment issue in key races across the country, setting up an even larger fight over what the operative termed "middle-class security"—that will include raising the minimum wage and other issues—in the fall.

Reid offered a preview of the Democratic messaging on the issue Thursday, telling the story of a 57-year-old woman from Nevada who has been forced to couch-surf while she looks for a job.

"[She has] worked from the time she was 18 years old. She's lost her job; she can't find a job. She's a long-term unemployed [person] .… She sold everything she has except her clunker of a car, all her personal things. She did that so, madam president, she could buy gas in case she gets an interview. People are just like this in every state. Our job is to do right by them. All we need is one more Republican vote to step up, do the right thing, and cross the aisle," Reid said on the Senate floor.

He told that same story three separate times on Thursday, an indication of just how heavily Democrats plan to push that personal messaging this year.

Republicans argue that they don't oppose unemployment insurance in general and are trying to find a path forward. They blame Reid for refusing to compromise. Their objections are twofold. First, it must be paid for. But, second, Senate Republicans want to have a chance at an open amendment process.

"Well, of course this is not about trying to find a solution; it's about trying to create an issue," Senator John Cornyn, who chaired the National Republican Senatorial Committee last cycle, said Thursday. "But I think we've demonstrated that it's Senator Reid who has foreclosed any debate or improvement of the legislation in a way that will actually help the unemployed … in terms of improving job training and access to things like Pell Grants and other funding that would actually help people acquire the skills that would help them qualify for a good, high-paying job."

It's a procedural issue that has many of GOP members up in arms about the way Reid is running the Senate, but may not translate as well to an electoral message as, say, a woman selling her earthly possessions so she can go to job interviews.