Top Senate Republicans are calling for President Trump to withdraw Andrew Puzder's nomination for Labor secretary, CNN reported Wednesday.

There are four Republican senators planning to vote against Puzder, and could be as many as 12, the report said, citing a GOP source. The GOP has a 52-seat majority in the Senate, so Puzder's nomination would fail if three or more Republicans joined all Democrats in opposing him.

EXCLUSIVE: Top Senate Rs have urged the WH to withdraw Puzder nomination. There are 4 firm no votes and up to 12, source says. Next on CNN — Manu Raju (@mkraju) February 15, 2017

The Senate is scheduled to hold a hearing this week for Puzder, a top target of opposition for Democrats.

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Senate Minority Leader Charles Schumer Chuck SchumerDemocrats scramble on COVID-19 relief amid division, Trump surprise Pelosi, Schumer 'encouraged' by Trump call for bigger coronavirus relief package Schumer, Sanders call for Senate panel to address election security MORE (D-N.Y.) urged the president to withdraw the nomination amid a growing controversy about Puzder hiring a housekeeper who was an undocumented immigrant.

Puzder, the chief executive of fast-food parent company CKE Restaurants, also faces other vulnerabilities. His wife once accused him of domestic violence — an accusation she has since retracted — and groups have attacked Puzder for the way workers are treated at his fast food restaurants

Sen. John Cornyn John CornynSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Republican Senators raise concerns over Oracle-TikTok deal MORE (R-Texas) earlier Wednesday remained confident about Puzder's nomination, telling reporters "he'll be confirmed."

Jordain Carney contributed.