WASHINGTON (NEXSTAR) — Recent messaging from White House advisors and top Republican lawmakers has centered around a second round of stimulus relief being targeted for those most impacted by the financial situation created by the COVID-19 pandemic. Could that means millions of Americans who received a check earlier this year being left out of round two?

Senate Majority Leader Mitch McConnell has said lawmakers will begin discussing a stimulus packages following the current two-week congressional recess. During a Monday event in Kentucky, McConnell noted a stimulus check could be included in the package — and it might be targeted to those hardest hit, according to The Washington Post.

“I think the people who have been hit the hardest are people who make about $40,000 a year or less,” he said.

Reporting from The Washington Post appears to show McConnell’s comments carry weight. The Post notes Republican leaders are examining proposals that drop stimulus check amounts below the $75,000 earning threshold in the first round of relief.

The report aligns with previous comments from Larry Kudlow, White House National Economic Council Director, who said “tax rebates or the direct mail checks” are being considered, but the priority of the government should be helping 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 toward the end of June. “That’s the speculation on my part, but I think … that’s where it’s going.”

Some argue dropping the payment threshold from round one’s $75,000 limit could negatively impact many Americans.

“To the extent they make it a lower income cutoff than the last time, it will hurt more people,” said Dorothy Brown, a tax expert and professor at Emory University School of Law, in an interview with The Washington Post. “This will have drastic human consequences.”

On Thursday morning, Steven Mnuchin, Secretary of the Treasury, said he was hopeful stimulus legislation could be passed by the end of July. That seems to echo President Trump who said earlier this week the next round of checks would be coming sooner than later.

“We are working on another stimulus package, and that will take place … very soon,” Trump told Jessi Turnure, a reporter for the Nexstar Washington, D.C. Bureau.

Trump said his administration and Congress are currently negotiating the exact amount included in the next round of coronavirus relief.

On Tuesday, a top aide to Vice President Mike Pence said the White House is looking at a second package totaling around $1 trillion.

“There’s obviously been a lot of stimulus put in the system over the last couple bills and so the price tag for us would be that,” Marc Short, Pence’s chief of staff, said during an interview on Bloomberg Radio.

Congress and the Senate will recess until July 20. It’s unlikely the Senate will consider any additional relief packages before that time.