Sen. Ben Sasse is also urging Attorney General William Barr to "rip up" the deal.
If confirmed, the son of late Supreme Court Justice Antonin Scalia would replace outgoing Secretary Alexander Acosta.
No other U.S. president has lost so many Cabinet members in his first term to ethics issues.
Acosta stepped down over the Jeffrey Epstein scandal, leaving Trump to find a new head for the Labor Department.
As a U.S. attorney in Miami, Acosta helped devise a secret agreement granting the accused child sex trafficker immunity from federal prosecution.
The centrist Democrat is having second thoughts about Labor Secretary Alex Acosta, who once helped sex offender Jeffrey Epstein avoid prosecution.
The labor secretary brokered a deal years ago that helped the financier avoid prison time for sex crimes with minors.
Courtney Wild said she feels like the prosecutors handling the convicted child sex offender's case today actually want "to take a predator off the street.”
“We have a president who is a sexual predator,” the longtime Republican insider said.
The president stood by his labor secretary, who approved a deal that allowed Epstein to avoid federal prosecution and significant prison time.
The senator called for the labor secretary to resign because he gave a secret plea deal to convicted child sex offender Jeffrey Epstein in 2008.
The Trump labor secretary and former U.S. attorney approved a 2008 plea deal that allowed the billionaire sex offender to avoid a possible life sentence.
Trump's labor secretary has come under renewed scrutiny for a secret 2008 plea deal he struck with billionaire sex offender Jeffrey Epstein.
He's a "terrific guy" and "fun," Trump told New York Magazine for a 2002 profile of his then-pal who faces sex trafficking charges.
Some of his victims still want their day in court.
The actor-artist's latest cartoon targets the financier convicted of operating a sex ring with underage girls.
The president claims he didn't know his labor secretary once made a secret plea deal with billionaire financier Jeffrey Epstein and kept it secret from the victims.
The federal prosecutors include Labor Secretary Alexander Acosta, who was the U.S. attorney in Miami at the time.
The Florida financier molested dozens of underage girls, according to a federal investigation.
The labor secretary reportedly brokered an outrageously lenient plea deal for an accused child sex trafficker.