President Trump and U.S. Sen. Elizabeth Warren went on the Twitter warpath yesterday — and they aren’t likely to bury the hatchet anytime soon, political observers say, as each has a lot of gain from their sparring going into the 2020 race.

“They have a common interest,” longtime former GOP consultant Todd Domke told the Herald. “Each side likes to use the other as a foil.”

Their long-running tit-for-tat tweet feud over Warren’s Indian heritage claim ramped up over the past couple of days after the Democratic senator released a DNA report showing she likely has a distant Native American ancestor.

“Pocahontas (the bad version), sometimes referred to as Elizabeth Warren, is getting slammed. She took a bogus DNA test and it showed that she may be 1/1024, far less than the average American. Now Cherokee Nation denies her, “DNA test is useless.” Even they don’t want her. Phony!” the president wrote in a three-tweet series bashing the senator.

Warren’s campaign, in one of a 26-tweet thread, responded “nicknames don’t help families pay for child care. Conspiracy theories won’t solve climate change. Racial slurs can’t raise wages or make our communities safer.”

So far, Republican and Democrats say Warren has more to gain.

GOP consultant Brad Marston told the Herald this keeps Warren in the headlines during the 2018 election cycle, when she otherwise would be pushed aside for more coverage of more competitive races.

“This puts her in the conversation,” Marston said, noting that the Fox News chyron as he spoke on the phone was “Warren DNA Disaster.” “It still says ‘Warren.’ Her name is up in the screen on national TV.”

Democratic political consultant Scott Ferson said, “Before you go high, I think a path to winning the nomination is to go low against Trump.” Ferson added, “Well, that’s the political answer. The real answer is ‘nobody wins.’”

Warren is widely expected to run for president in 2020, saying she will “take a hard look” at a presidential bid against Trump, who has frequently mocked Warren’s claims of Native American ancestry.

The latest campaign finance data shows Warren has an eye on some of the key opening primary states of the 2020 round; last month she gave $5,000 to each of the state Democratic parties of South Carolina and Iowa, and $5,000 each to parties in states with tight Senate races this year such as Florida, Nevada and West Virginia.

Ferson said that’s a good way for presidential hopefuls to build a foothold for themselves before running.

“It’s not just a common strategy — it’s a proven winner,” Ferson said.

— sean.cotter@bostonherald.com