Kevin McCarthy allies privately push moderate Democrat to switch parties in House speaker bid

In a sign of the challenges House Minority Leader Kevin McCarthy faces to secure enough votes to possibly become the next speaker of the House, his allies have tried to persuade one moderate Democrat to switch parties.

Democratic Texas Rep. Henry Cuellar said he received multiple calls from people close to McCarthy, including one current Republican member.

What was the pitch? "Name your price," Cuellar told ABC News.

He said his response was simple: "No, thank you."

"I mean, they see me as a moderate Democrat so they think he's probably somebody that will consider it," Cuellar said when asked why Republicans would call him.

Cuellar said McCarthy did not reach out to him personally.

McCarthy's office said In a statement, "As a standard rule we do not discuss private conversations between members of Congress. However, Congressman Cuellar is a lifelong Democrat and will remain a Democrat. Period."

Speaking about Republicans' effort to get Cuellar to switch parties, House Democratic Caucus Chair Hakeem Jeffries blasted Republicans for having "nerve" -- wanting it both ways.

"They literally just spent millions of dollars mischaracterizing Henry Culler's leadership, then get wiped out by Cuellar and Vicente González and want to run to them, saying 'we need your help,'" Jeffries said.

Cuellar is projected to retain his seat in Texas' 28th Congressional District, located along the Mexican border in the southwest part of the state. He leads Republican Cassy Garcia by about 22,000 votes.

While votes are still being counted in several key House races, Republicans are inching closer to the majority. If the GOP takes the majority in the House, McCarthy will need 218 votes on the floor in January to secure the position of speaker, the highest-ranking Republican and second in line to the presidency.