On Friday, it was Labor Secretary Tom Perez's turn to make the case:
"The important thing to understand here is, this is not only the right thing to do, but it's the smart thing to do, because the people who are getting this money, they're not investing in some offshore bank account, they're spending it on the basic necessities of life. So if you refuse to extend it, you're actually digging the hole further."
The Congressional Budget Office has estimated that a three-month extension of emergency unemployment benefits would cost $6.55 billion.
"There is a long, proud, bipartisan history of expanding emergency unemployment benefits during times like this," Perez said. Although the unemployment rate dropped to 7 percent in November, "We have more work to do," he admitted.
"This is the difference between hardship and catastrophe. They're already struggling through no fault of their own. And the people who lost this lifeline -- they can't feed their family. It's not fair."
Asked if the Obama administration would be open to offsetting the cost of extending the benefits, Perez said, "We want to find a solution that works."
'People aren't getting rich on this'
On Thursday, Gene Sperling, director of the White House National Economic Council, appeared on various news shows to urge a three-month extension of unemployment benefits for the 1.3 million Americans who exhausted their 26 weeks of state benefits on Dec. 28.
Sperling said a short-term extension "will give us more time to figure out a solution for all of 2014." The price tag for a full-year extension is around $25 billion.
Sens. Dean Heller (R-Nev.) and Jack Reed (D-R.I.) have introduced a bill that Senate Majority Leader Harry Reid reportedly plans to bring to a vote on Monday.
"If we move quickly, we can prevent a lot of hardship. We can prevent a lot of these families from going through a gap," Sperling said.
"People aren't getting rich on this," he told MSNBC's Andrea Mitchell. "This is maybe 2 (hundred dollars), $300 a week. This is the basic support people use for their families. And this is very important."
Sperling noted that people are eligible for emergency benefits, only it if they are actively looking for a job; and the benefit "naturally tapers off -- or it's designed to taper off" -- as the economy improves.
"This is there for those places across the country right now where there is a real almost historic problem with long-term unemployment. And this is the least we can do. And the most we can do is do a lot more to create jobs in 2014..."
Sperling's prescription for job-creation is to combine tax reform with an infrastructure bill: "That's the type of grand bargain on jobs that would do more in the long term to create more jobs and help more of those long-term unemployed have a place to go."
On the other side of the argument, Cato Institute economist Chris Edwards told CNN that people have known for a long time that their 26 weeks of unemployment benefits were going to expire:
"People should have been making the tough decisions they needed to make to find a job. And the problem when the welfare state gets too expansive is that people tend to depend too much on government," Edwards said.
"The message for the future I think is that individuals need to save more, to put away money for possible recessions in the future."