Congresswoman Maxine Waters speaking at the CNBC Capital Exchange event in Washington, D.C. on July 25th, 2018. David A. Grogan | CNBC

The top Democrat on the House Financial Services Committee sent a message to the party's progressive wing on Wednesday, distancing herself from the vocal lawmakers to her left as the party continues to debate its message ahead of the November midterm elections. "The Democratic Party is not a socialist party," California Rep. Maxine Waters said in an interview with John Harwood at CNBC's Capital Exchange event Wednesday. Asked about left-wing politicians who identify as democratic socialists, including 2016 presidential candidate Sen. Bernie Sanders, I-Vt., Waters said: "I just don't think our party should be identified because we have a few people who seem to be to the left of the left." Democrats continue to face down lingering anxiety about the identity of their party, as Republicans, including President Donald Trump, seek to leverage the internal rifts over economic and social issues to their own electoral advantage. The president has zeroed in on Waters, painting her in posts on Twitter as the “unhinged FACE of the Democrat Party.”

Battling with Trump

Waters is one of Trump’s most outspoken critics in Congress, and often has called for the president’s impeachment. The president has responded by calling Waters "crazy" and an "extraordinarily low IQ person." On Wednesday, Waters said she ignored the president's attacks. "I don’t care what he calls me. I know who I am. I know what I do," Waters said. "I am perfectly comfortable with me. He can call me whatever he wants to, he does not intimidate me, and I am not going to stop talking about him." Waters' high-profile calls to impeach the president and publicly confront members of the administration have made her a polarizing figure. She and her staff have faced a number of threats to their safety. On Tuesday, her office in Los Angeles was evacuated after a staffer found a package addressed to “Anne Thrax,” the Los Angeles Times reported. Officials later deemed the stunt a hoax. Separately, last week a man was sentenced to three years of probation for threatening in a voicemail to kill Waters. "If you continue to make threats toward the president, you're going to wind up dead, Maxine, 'cause we'll kill you," the man, Anthony Scott Lloyd, said in the recorded message, according to NBC Los Angeles. Waters has remained defiant in the face of the threats. “And I know that there are those who are talking about censuring me, talking about kicking me out of Congress, talking about shooting me, talking about hanging me,” she said at a June rally. “All I have to say is this: If you shoot me, you better shoot straight. There's nothing like a wounded animal.”

Waters calls for ICE reform, not abolishment

Waters differs from left-wing Democrats on another issue, too: calls to abolish Immigration and Customs Enforcement, or ICE. She said Wednesday that she disagreed with people calling for an end to the agency, which has become a source of controversy while Trump pursues hardline immigration policies. "Those people who decided and took the position that it had to be abolished did not think it through in ways that said it has to be reformed," she said. Trump has slammed Democrats over calls from some members of the party to end ICE. At a rally in Kansas City on Tuesday, Trump called Democrats who favor abolishing ICE Waters' "disciples." He said he looked forward to Democrats raising the issue during the midterms as well as during his next presidential campaign. "I hope they keep it up, because we're going to have a lot of fun in four months and we're going to have a lot of fun in 2020 running against that," the president said at the rally. A number of Democrats have called for the elimination of the agency, including Sens. Kirsten Gillibrand of New York and Elizabeth Warren of Massachusetts. Alexandria Ocasio-Cortez, the high-profile democratic socialist who defeated Rep. Joe Crowley in his New York primary election last month, ran on a platform of getting rid of ICE.

Capitalism, but with limits