But the math doesn't add up, according to economists. There are likely millions more people out of work than there are open jobs.
Those on the losing end of this equation could face an extreme drop in income next month if the unemployment supplement — an extra $600 a week — expires as scheduled.
"It's not going to work in every case," Ernie Tedeschi, a labor economist at Evercore ISI, said of the back-to-work-bonus concept. "There aren't nearly enough jobs available out there for people to take."
"It might work in some instances, but it won't be the silver bullet that heals the economy," he added.
The employment picture improved over the past two months, as states began reopening their economies.
Businesses added 7.5 million jobs to their payrolls over May and June, following a historic loss of more than 22 million jobs in the two prior months, according to the Bureau of Labor Statistics.
April's 14.7% unemployment rate, the peak during the coronavirus pandemic, was the country's worst since the Great Depression.
It has since recovered to 11.1% — still worse than any other period in the modern era.
Republican officials have seized on the rebound to argue that enhanced unemployment aid should end. That $600-a-week benefit expires after July 31.
Democrats want to extend it as part of another round of coronavirus relief.
"We won't be doing it in the same way," Treasury Secretary Steven Mnuchin said Thursday of the $600 supplement. "We're in a dramatically different situation."
"Many businesses are open," he added. "Many businesses want to hire more people today."
"We've recreated 8 million jobs in the last two months," Mnuchin said.
Republicans don't yet appear to have coalesced around one policy. Some want to replace the enhanced unemployment benefits with a back-to-work cash bonus for those who find jobs.
Sen. Rob Portman, R-Ohio, proposed replacing the $600 weekly checks with temporary payments of $450 a week for those who return to work, for example. Recipients would get the $450 plus their regular wages.
A plan from Rep. Kevin Brady, R-Texas, would pay workers the equivalent of a $1,200 hiring bonus.
Republican lawmakers have said the $600-a-week unemployment supplement, which is in addition to standard state benefits, offers a disincentive to work.
But these back-to-work bonuses would only benefit those who can find jobs — and it doesn't seem there are enough to go around.
There were 5.4 million job openings on the last business day in May, according to data published last Tuesday by the Bureau of Labor Statistics.
But there are nearly 18 million unemployed Americans, according to the bureau — or more than three times the number of available jobs.
"A return-to-work bonus is an inappropriate policy solution," Beth Akers, a former staff economist on Council of Economic Advisors under former President George W. Bush, said of the current situation.
"It's definitely the case there are fewer jobs open in the economy right now than there are people willing, able and interested in those jobs," said Akers, a senior fellow at the Manhattan Institute.
The number of job openings may also be leveling off or shrinking. Officials in states like California, Nevada and Texas have ordered some businesses to close for a second time, due to spiking coronavirus infections.
Those unable to find a new job would experience a "cliff in disposable income" if the $600 weekly unemployment benefit isn't extended, Akers said.
Absent the $600 supplement, standard state unemployment benefits would only replace about a third of workers' lost wages, according to a report published this year by the W.E. Upjohn Institute for Employment Research.
Ideally, Congress would legislate (and states would be able to implement) an unemployment subsidy that — unlike the current one — doesn't exceed a worker's lost wages, Akers said.
But letting aid expire completely after July for the unemployed is "definitely something we don't want to happen," she said.
There are some caveats.
For one, data on job openings and the number of unemployed is derived from two different surveys conducted by the Bureau of Labor Statistics, so the figures don't necessarily align perfectly, economists said.
Further, the number of unemployed includes 10.6 million people who were furloughed, or temporarily laid off, by their employer. That's nearly 60% of the total unemployed.
Businesses wouldn't necessarily post a job opening for an employee who's been temporarily laid off — they'd likely just try contacting that person and bringing them back to work, Tedeschi said.
However, one measure of "permanent" layoffs still appears to exceed job openings by about double, Tedeschi said.
When stripping out furloughed workers, there are about 7.2 million unemployed.
But there are another 8.2 million Americans who aren't in the labor force but want a job, according to the Bureau of Labor Statistics. They may, for example, have temporarily sidelined themselves from the labor market due to the pandemic but aren't technically labeled as "unemployed."
While the ratio of this measure of permanent unemployment compared with job openings is now about 2:1, it was roughly 1:1 in February before the pandemic hit the U.S., Tedeschi said.
"Even if you adjust for temporary layoffs, there are still way more unemployed people or nonemployed people than there are job openings," he said.