FIRST ON FOX: A new bill could designate unused federal COVID-19 funds to be used to continue the construction of the southern border wall as an illegal immigration crisis continues and voters cite the issue as one of the most important going into the November elections.

Senate Republican Conference Chairman John Barrasso, R-Wyo., introduced an amendment on Tuesday to a Democrat-backed border bill that is set to come back to the floor later this week. 

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Titled "The Build the Wall Act of 2024," the measure would create a "Southern Border Wall Construction Fund" and instruct the Department of Homeland Security to use unobligated funds that were initially authorized for pandemic recovery. 

"Border walls work. Before President Biden came into office, we were well on our way to a secure and safe southern border. But on his first day in office, the president and Democrats rolled out the welcome mat for millions of illegal immigrants to come into our nation," Barrasso said in a statement. 

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"We must hold Democrats accountable for their open border policies that have created the worst border crisis in our nation’s history. If they are serious about securing our border, they should have no issues voting for a policy that actually works and is already paid for," he continued. 

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The Democrat-backed border bill is expected to fail a test vote this week. GOP senators rejected the measure as too weak after it was negotiated by Sens. Chris Murphy, D-Conn., Kyrsten Sinema, I-Ariz., and James Lankford, R-Okla. Some even claimed the immigration bill would make the current border crisis worse. Republicans have reaffirmed their backing of a tougher House-backed immigration measure, known as H.R. 2.

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Barrasso's proposal to use unspent COVID-19 relief money for the wall comes after Republicans criticized the Department of Treasury's latest guidance on the COVID-19 State and Local Fiscal Recovery Funds granted in President Biden's much touted American Rescue Plan. 

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In March, the department changed its guidance in regard to the unspent COVID-19 relief funds, stating "that qualifying recipients can use remaining funds on a broad range of uses to fund affordable housing serving very low-income families." 

Republicans sought to prevent the change last week, but they were blocked in the Senate by Democrats in a party-line vote.