Ever since Congress left town for the holidays in December without renewing emergency unemployment payments for the long-term unemployed, Democrats have been hammering Republicans to take up a bill that would do just that. On Tuesday, to the surprise of those leading the charge, the U.S. Senate inched closer to a vote on a measure that would add another three months of benefits for those who have exhausted their federal emergency unemployment insurance without finding another job.

In the Senate, the Emergency Unemployment Compensation Extension Act (S. 1845), a measure co-sponsored by Sens. Jack Reed (D-RI) and Dean Heller (R-NV), faced a filibuster unless Democrats could find an additional five Republicans to vote with them on a cloture motion. Prospects were dicey, right up until the last minute.

“It was in the balance until the very last moment,” Reed said at a press conference following the vote. “I was hopeful, but I guess being Irish I’m always expecting the worst.”

Of the six Republicans who joined the Democrats in forestalling a filibuster on the bill were three of the Republicans’ four women senators: Kelly Ayotte (NH), Susan Collins (ME), and Lisa Murkowski (AK). Rob Portman (OH), Dan Coats (IN), and, of course, co-sponsor Heller rounded out the GOP’s filibuster-busting contingent.

Immediately following the vote, President Barack Obama staged a press event in the East Room of the White House, his podium placed against a backdrop of unemployed Americans standing on risers. Introducing the president was Katherine Hackett of Moodus, Connecticut, who described herself as the mother of two grown sons who are serving in the military.

The event was designed to refute the claims of Republicans such as Sen. Rand Paul (KY), who recently claimed, during an appearance on Fox News Sunday last month, that an extension of unemployment benefits to the long-term unemployed was a “disservice” to those who are out of work because, he claimed, it encouraged them not to look for jobs. Never mind that, according to economist and former Labor Secretary Robert Reich, who spoke to reporters on a press conference call arranged by House Democrats on Friday, there are at least three unemployed workers for every available job.

“I have cut expenses everywhere possible,” Hackett said at Obama’s press event, “and I am not just sitting at home enjoying the good life. My cuts include heating my house to 58 degrees, wearing a hat and a coat to stay warm, because oil is expensive. I have lost weight, because food is expensive.”

Hackett went on to describe how, as a single mother, she raised two sons, “working many different jobs, never asking for a handout.”

Single mothers are overrepresented among the ranks of the long-term unemployed, according to the National Women’s Law Project, which reported an unemployment rate in June among single mothers of 10.7 percent (compared with 7.0 percent that month for the general population). Older workers and African-Americans also disproportionately comprise the ranks of people who have been out of work for more than six months, as do those who did not attend college.

Obama took on the Republican rhetoric launched in opposition to an extension of unemployment benefits by saying he had never met an American who would rather have an unemployment check than a job.

“They’re not looking for pity,” he said. “They just want a shot.”

He also noted that despite GOP arguments that extended unemployment benefits somehow hurt the economy, they actually act as a stimulus, since the unemployed spend the benefit money right away on necessities, and he called on the House of Representatives to act speedily on the unemployment extension as the Senate proceeds with its votes on the measure.

“Voting for unemployment insurance helps people and creates jobs,” the president said. “Voting against it does not.”

(Some critics of the GOP suggest that the stimulative effect just might be the real impetus behind Republican opposition to the extension, since it could help improve the economy on the president’s watch, ahead of the 2014 midterm elections.)

Despite the fact that emergency unemployment insurance extensions traditionally pass without additional burdens attached, Republicans are demanding an “offset” to pay for any extension they may vote for.

Speaking on the floor ahead of the cloture vote, Senate Minority Leader Mitch McConnell (R-KY) suggested that in exchange for an extension of emergency unemployment benefits, Democrats should accept a one-year delay in the imposition of the individual mandate in the Affordable Care Act. While that’s not likely to happen, Democrats, while balking at the notion of offsets, have made noises to the effect that they might consider the closing of corporate tax loopholes as a means of paying for the extension of benefits. On a teleconference with reporters on Sunday, Sen. Charles Schumer (D-NY) suggested eliminating tax breaks “for corporations shipping jobs overseas.”

Despite Tuesday’s vote, chances for passage of the unemployment extension remain uncertain. But Republicans are surely feeling the heat.