An apology from Ted CruzRafael (Ted) Edward CruzDemocrats question fairness of Senate trial after Graham, McConnell statements Sunday shows - Republicans, Democrats maneuver ahead of House impeachment vote Cruz says he intends to 'fully' follow impeachment oath MORE for calling Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellDems want tougher language on election security in defense bill Schumer asks McConnell for Mulvaney, Bolton to testify in impeachment trial Democrats question fairness of Senate trial after Graham, McConnell statements MORE a liar "ain’t gonna happen," the presidential hopeful said during a Thursday interview with CNN's Dana Bash.  

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"If the Washington lobbyists want to see that happen, they can hold their breath a long, long time," Cruz said. "My focus is on the American people." 

Last summer, Cruz made headlines when he accused McConnell of lying to him over a deal to vote on reauthorizing the Export-Import Bank. 

He brushed aside suggestions from Bash that an apology could help unite more Republicans behind him in his race for the party's nomination. 

"This is why people are so frustrated with Washington," Cruz said. "It's the inside battles back and forth. This isn't a game. This isn't about Washington power brokers. This isn't a smoke-filled room."