#2020Vision: Warren talks 'Pocahontas' while Booker, Gillibrand swear off corporate cash

Sen. Elizabeth Warren addressed President Donald Trump's nickname for her, "Pocahontas," this week.

Washington (CNN)Our weekly roundup of the news, notes and chatter about the prospects for the next Democratic presidential race:

A trio of 2020 prospects moved to clean up potential problem spots this week.
Massachusetts Sen. Elizabeth Warren defended her claims of Native American heritage and responded to the nickname President Donald Trump uses to refer to her -- "Pocahontas" -- in a surprise appearance Wednesday at a National Congress of American Indians event. In addressing her previous claims of Native American heritage, she dove into a story about growing up in Oklahoma, where her mother's family was part Cherokee.
"They're gone, but the love they shared, the struggles they endured, the family they built and the story they lived will always be a part of me. And no one -- not even the President of the United States -- will ever take that part of me away," she said.
    On Tuesday afternoon, Sen. Kirsten Gillibrand announced in a tweet that she would "no longer accept donations from corporate PACs," then explained the decision -- and touted her record on a variety of related issues -- in a 60-second video. Later in the day, Sen. Cory Booker tweeted that he would follow suit. "I heard from constituents today asking about corporate PAC contributions," he wrote. "I'm joining several of my colleagues & no longer accepting these contributions." The moves by two strong fundraisers reflected the changing Democratic fundraising reality and dangers of being viewed as too close with corporate America.
    The junior senators from New York and New Jersey become the fourth and fifth Democratic senators to join this (mostly) ambitious caucus, following Sens. Warren, Bernie Sanders -- a Vermont independent who caucuses with the Democrats -- and Maria Cantwell of Washington state.
    (In related news, Gillibrand on Wednesday announced she would cosponsor Booker's Marijuana Justice Act, which would legalize pot at the federal level and, among other things, wipe clean past convictions for possession or use.)
    We're approaching the spring training portion of the 2020 presidential race. Nothing's officially underway, but prospective candidates are doing some big-picture planning, using 2018 races to road-test their sales pitches and looking for ways to clean up problematic issues before things get serious. A few other examples:
    • Former Vice President Joe Biden admitted mistakes in his handling of Anita Hill's testimony in 1991 alleging she had been sexually harassed by Supreme Court nominee Clarence Thomas.
    • Sanders -- who showed up at the NAACP's convention in Baltimore last year -- is being urged to court black voters by supporters gaming out a 2020 strategy.
    • Booker put a "pause" on raising money from the pharmaceutical industry -- although that cleanup effort came off a bit more nakedly political than he would have liked.

    News and notes:

    BERNIE'S MIDWESTERN TOUR, PT. ???: Bernie Sanders will hit three crucial 2020 states next week, as he sets out first for Illinois, then visits Iowa, Wisconsin and Michigan. Here's the schedule: First stop is next Thursday in Chicago, where Sanders will boost Chuy García, who's running to replace retiring Rep. Luis Gutiérrez, himself another potential 2020 player, in Illinois' 4th District. Next Friday, Sanders will be in Des Moines, Iowa, for a rally with campaign aide turned congressional candidate Pete D'Alessandro. Then it's a two-hour ride east to Cedar Rapids, for the first of three events (in three days) with progressive groups trying to turn the Trump tax cuts against Republicans. On Saturday, it's off to Wisconsin, first to appear with Randy "Iron Stache" Bryce, who's using his run in House Speaker Paul Ryan's 1st District as a platform to hammer the whole GOP Congress. Then it's up to Green Bay for another tax rally. The tour ends in Lansing, Michigan, on Sunday, for another rally with the "Not One Penny" tax tour.
    HARRIS VOTES AGAINST IMMIGRATION BILL: California Sen. Kamala Harris was one of three Democrats to vote against the failed immigration bill this week. She said in a statement that "while I applaud the work of my colleagues on the King-Rounds proposal, as a senator from the state with the largest documented and undocumented immigrant population, I could not in good conscience support it. While this bill would put Dreamers on a pathway toward citizenship, the appropriation of $25 billion for a border wall is a waste of taxpayer money."
    Bernie Sanders' evolution on immigration -- from voting against a George W. Bush-era comprehensive plan to now -- is also worth tracking, as The Washington Post's James Hohmann does here. Sanders called a border wall a "totally absurd idea," but said he's willing to pony up for border security. "I would go much further than I think is right," he said. "Unwillingly. Unhappily. I think it's a stupid thing to do. But we have to protect the Dreamers. ... I'm willing to make some painful concessions."
    MAYORS TO SOUTH CAROLINA: Los Angeles Mayor Eric Garcetti and South Bend, Indiana, Mayor Pete Buttigieg will be in Columbia, South Carolina, on Tuesday and Wednesday for an event on local infrastructure. Garcetti is expected to headline a South Carolina Democratic Party fundraiser on Thursday.
    In other early-state travel news: Former Missouri Secretary of State Jason Kander is headed back to New Hampshire on Tuesday to oppose GOP bills that impose more restrictive voting requirements.
    MURPHY ON GUNS: Connecticut Sen. Chris Murphy -- a leading advocate for gun control since the 2012 Sandy Hook shooting -- was on the Senate floor within hours of the Parkland, Florida, shooting, blaming Congress for inaction. "This epidemic of mass slaughter, this scourge of school shooting after school shooting," Murphy said, "it only happens here not because of coincidence, not because of bad luck, but as a consequence of our inaction. We are responsible for a level of mass atrocity that happens in this country with zero parallel anywhere else."
    NEW POLLS UNDERLINE DEMS' TRUMP/RUSSIA PICKLE: On Tuesday, the Democratic super PAC Priorities USA released new polling that showed President Donald Trump's favorability up a few points from November. But their big takeaway: Keep calm and don't get wrapped up in his daily drama. "Democrats continue to have winning messages on health care and the economy, but right now voters are not hearing them," the group said in a memo attached to the survey. "That must change."
    Fast-forward to Thursday and another liberal group, Stand Up America, made some headlines with a poll showing across-the-board support for special counsel Robert Mueller's investigation. And that, as McClatchy's Alex Roarty writes, is the kind of news that could "fuel the debate now dividing the party between a focus on pocketbook issues in 2018 or a campaign that pushes social issues and reacts to Trump."
    "IS THERE ROOM FOR ANTI-ABORTION DEMOCRATS?" That was the question posed to DNC chairman Tom Perez this week during an interview with MSNBC's Kasie Hunt. At issue, the primary challenge to anti-abortion Rep. Dan Lipinski from abortion rights supporter Marie Newman in Illinois' 3rd District. Perez answered: "There's a very spirited debate in that particular race, and so one thing I've learned from watching presidential politics is that when the DNC gets involved in Democratic primaries..." (At this point, Hunt noted that Lipinski is an incumbent.)
    Perez continued: "Well, again, one thing I've learned from primaries in the past is that when the DNC gets involved in those races, then we sometimes get accused of trying to put the thumb on the scale. That's one of those races where we will see what happens." For once, the messy 2016 primary comes to the aid of a party leader under pressure!

    From the right:

    KASICH'S TWO PATHS: Ohio Gov. John Kasich is considering two paths to challenge President Donald Trump in 2020, BuzzFeed's Cleveland-based Kasich whisperer, Henry Gomez, reports: primarying Trump or running as an independent. Some of Kasich's decisions around 2018 endorsements -- including encouraging Steve Poinzer in California to run as an independent for state insurance commissioner -- reflect that. "I think we are all watching things closely," Bob Klaffky, a member of Kasich's inner circle, told Gomez. "This is just my opinion, but I think the time could be right for an independent bid. I think there's a growing middle."
    A Kasich speech to watch will be May 23, when he delivers the Harvard Kennedy School of Government's commencement address.

    Before you go:

    Former Attorney General Eric Holder will keynote an Ohio Democratic Party dinner in Columbus on April 13. ... New Orleans Mayor Mitch Landrieu says as he leaves office, he is "going to take a rest and clear my head and think about ways to continue to serve, which is really in my blood." ... Buddies Eric Garcetti and Justin Trudeau went on a hike through Griffith Park in Los Angeles together, and posted pictures.