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WASHINGTON (NEXSTAR) — Despite President Donald Trump’s recent comments suggesting that a “very generous” second round of economic relief payments to Americans may be on the way, it’s unclear when, how and if that might happen.

“We will be doing another stimulus package,” President Trump said in an interview last week.

The president offered few details, however, saying, “It will be very good. It’ll be very generous.”

When asked how much the payment might be, Trump said, “You’ll find out about it. You’ll find out.” Trump added that he thought the relief funds would receive bipartisan support and could be announced “over the next couple of weeks.”

“It is going to happen, it’s just not going to happen yet,” Oklahoma Republican Sen. Jim Inhofe recently told Nexstar Media Group Washington D.C. correspondent Anna Wiernicki.

The Senator says the idea of a second stimulus check filled two-hours of discussion at this week’s Senate Republican luncheon. He added lawmakers are supportive but are still working on the details.

“What you don’t want to do is have a reward given to people who don’t want to work,” Inhofe added.

Texas Republican Senator John Cornyn says a payroll tax holiday is also being considered.

“That is a little challenging, because the payroll tax is how we pay for Medicare and Social Security — but that would be a way to get money directly in the hands of people who need the cash,” said Cornyn.

Democratic lawmakers appear more inclined to quickly distribute relief to Americans. Illinois Congressman Jesus Garcia argued payments are necessary because the pandemic is far from over.

“Without a doubt, we owe it to the American people,” said Garcia. “The high unemployment rates across the country argue for at least one more stimulus check and an extension of unemployment insurance benefits.”

Proposals on the table

In late March, President Trump signed a stimulus package into law that included one-time payments of up to $1,200 for eligible Americans. As the weeks have turned into months since the Coronavirus Aid, Relief, and Economic Security (CARES) Act was passed, many Americans are wondering if, and when, a second check or prepaid debit card will arrive as the pandemic continues.

The HEROES Act was passed by House Democrats in May and would offer another round of $1,200 checks to American adults and children. It also expands the number of people who are eligible to receive government aid by including college students and older teenagers. The payments would be capped at $6,000 per household.

White House advisor wants payment to get to people ‘most in need’

Larry Kudlow, who serves as director of the White House National Economic Council, told Fox News Business on Tuesday he thinks “tax rebates or the direct mail checks” are being considered, but he said he believes the government should target out-of-work Americans.

“Probably, we would want to target those to those folks who lost their jobs and are most in need,” Kudlow told Fox News Business. “That’s the speculation on my part, but I think … that’s where it’s going.”

Kudlow said Trump wants “incentive-oriented policies” such as a payroll tax holiday to get people back to work. He added President Trump is considering deductions for restaurants, entertainment, tourism and sightseeing.

When pushed, Kudlow said he thought the tax rebates or direct mail payments “are on the table” but qualified the statement by saying that they are still in a “pre-decisional” phase.

“We want this to be a constructive package,” Kudlow said. “It may be that the tax rebates are part of that. I don’t want to say for sure… I don’t want to say for not… but I know it’s on the table.”

Critical jobs report coming this week

A new report from The Hill says additional financial support may hinge on a jobs report being released this week.

May’s report showed the country gained 2.5 million jobs. If that trends continues in June, many analysts feel lawmakers would move past a second round of stimulus checks pointing to early signs of an economic recovery.

The Hill reports lawmakers would be more likely to extend increased unemployment benefits that are currently slated to sunset at the end of July.

“They don’t see the market crashing, they see a better-than-expected jobs report last month, and so their focus is very much targeted [around a] back-to-work narrative,” said Ben Koltun, a senior research analyst at Washington’s Beacon Policy Advisors, in an interview with The Hill. “If there’s a bad jobs report — and when you see more people out of work than last month — then there may be an impetus by more Republicans in the conference to provide broader support and more stimulus spending than they’re talking about right now.”

The Associated Press contributed to this report