The running fight between U.N. Ambassador Susan Rice and congressional Republicans escalated Tuesday, with key senators vowing to block Rice’s nomination if President Barack Obama ever decides to pick her as his next secretary of state.

Rice headed to the Capitol on Tuesday morning to meet with three key GOP voices on foreign policy and discuss the deadly Sept. 11 attacks in Benghazi, Libya. But despite some softer rhetoric from Republicans over the weekend, the meeting ended badly, with Sen. John McCain and two other GOP senators saying they were “significantly troubled” by Rice’s explanation of the attacks.