Progressives are warning South Bend, Ind., Mayor Pete Buttigieg Pete ButtigiegBillionaire who donated to Trump in 2016 donates to Biden The Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November Buttigieg stands in as Pence for Harris's debate practice MORE not to attack Sen. Elizabeth Warren Elizabeth WarrenOvernight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds On The Money: Half of states deplete funds for Trump's 0 unemployment expansion | EU appealing ruling in Apple tax case | House Democrats include more aid for airlines in coronavirus package Warren, Khanna request IG investigation into Pentagon's use of coronavirus funds MORE (D-Mass.) at Tuesday night’s Democratic debate in Ohio.

Buttigieg, who has emerged as a center-left contender for the Democratic presidential nomination, has drawn the ire of progressives in recent days for remarks viewed as swipes against more liberal contenders like Warren and former Rep. Beto O’Rourke (D-Texas).

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“It’s sad to see the potential self destruction of @PeteButtigieg, a rising star,” tweeted Adam Green, a cofounder of the Progressive Change Campaign Committee, which backs Warren. “Tuesday will be a key trajectory moment. Does he attack the next President of The United States or take the high road and make positive waves by adding his unique voice to progressive issues of the day?”

The warning comes as Buttigieg has been rising in Iowa polls, positioning him to become a potential top-tier challenger to Warren and former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE.

A Firehouse-Optimus poll released Monday found Warren at 25 percent support in Iowa, followed by Biden at 23 percent and Buttigieg at 17 percent. In the past month, Buttigieg’s support in the state has jumped nearly 5 percentage points in the RealClearPolitics average, putting him in contention with Warren, Biden and Sen. Bernie Sanders Bernie SandersSirota reacts to report of harassment, doxing by Harris supporters Republicans not immune to the malady that hobbled Democrats The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election MORE (I-Vt.).

Progressives on Monday seized on remarks Buttigieg made to Snapchat’s Peter Hamby, in which he was asked about Warren’s pledge to refuse money from high-dollar donors. Warren raised $24.6 million in the third quarter, compared to $19.1 million for Buttigieg.

"My competitors can go with whatever strategy they like, but we're going to make sure that we have the resources to compete because we are going up against the sitting president of the United States,” Buttigieg said.

“He has tremendous amounts of support and allies at his back, and we're not going to beat him with pocket change. I'm proud of the fact that we have more than half a million individuals who've supported my campaign. Some of it's chipping in three bucks; some of it's a lot more. I think you need the full spectrum of support in order to compete, especially if we want to go against someone like Donald Trump."

Buttigieg’s allies say he was not taking a swipe at Warren, but rather was making the argument that the Democratic nominee will feel an urgency to compete on the money front against President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE and the Republican National Committee, who combined to raise $125 million in the third quarter.

But some liberals viewed Buttigieg’s remarks as disparaging toward Warren and small-dollar donors.

"This is legit insulting to the millions of folks who are participating in the process and giving what they can. And -- it should be noted -- small-dollar donors powered the two candidates who out raised Pete last quarter,” tweeted progressive strategist Rebecca Katz.

Meanwhile, some progressives are lashing out at Buttigieg after he clashed with O’Rourke, who has advocated for a mandatory gun buyback program.

Buttigieg called such proposals a “shiny object” that will distract Washington from achieving more realistic gun safety reforms.

"As a policy, it's had mixed results," Buttigieg said. "It's a healthy debate to have, but we've got to do something now."

Sen. Cory Booker Cory Anthony BookerThe movement to reform animal agriculture has reached a tipping point Watchdog confirms State Dept. canceled award for journalist who criticized Trump 3 reasons why Biden is misreading the politics of court packing MORE (D-N.J.), who will also be on stage for Tuesday’s debate, accused Buttigeig of “doing the NRA’s work for them.”

Buttigieg has also sought to draw distinctions between himself and Warren on health care, releasing a “Medicare for those who want it” plan to contrast with the “Medicare for All” plan backed by Warren and Sanders.