Nearly one month into his tenure in the White House, President Biden has been able to keep the peace with the progressive wing of the Democratic Party.

But comments on the issues of student loan forgiveness, defunding the police, and how quickly to raise the minimum wage that the president made during a town hall Tuesday night in Milwaukee, Wis., that was hosted by CNN are anything but welcome signals for progressives.

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A leader in the progressive movement warned that Biden’s comments at the town hall could damage grassroots support for the president’s COVID relief plan, which he aims to have passed through Congress and signed into law in the coming weeks.

"I'm not sure Biden fully understands that every time he throws cold water on a popular progressive idea, it hurts grassroots enthusiasm and activism for other parts of his agenda like COVID relief and millions of clean-energy and infrastructure jobs," Progressive Change Campaign Committee co-founder Adam Green told Fox News.

President Joe Biden stands on stage during a break in a televised town hall event at Pabst Theater, Tuesday, Feb. 16, 2021, in Milwaukee. (AP Photo/Evan Vucci)

President Joe Biden stands on stage during a break in a televised town hall event at Pabst Theater, Tuesday, Feb. 16, 2021, in Milwaukee. (AP Photo/Evan Vucci) ((AP Photo/Evan Vucci))

Biden clearly shot down a push by Senate Majority Leader Chuck Schumer and other prominent congressional Democrats to wipe out up to $50,000 in federal student loan debt to all borrowers.

An audience member at the town hall, urging Biden to commit to cancel up to $50,000 in debt, asked, "What will you do to make that happen?"

"I will not make that happen," the president answered.

Biden explained that he believes he can't eliminate $50,000 on his own without action by Congress.

"I understand the impact of debt, and it can be debilitating," Biden said. "I am prepared to write off the $10,000 debt but not $50 [thousand], because I don't think I have the authority to do it."

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Some of the best-known progressives in Congress – including Sen. Elizabeth Warren of Massachusetts and Reps. Ayanna Pressley of Massachusetts and Ilhan Omar of Minnesota -- support the bill being pushed by Schumer.

Schumer and Warren - in a statement on Wednesday - noted that Presidents Obama and Trump used their executive authority to cancel student loan debt.

"It's time to act. We will keep fighting," they wrote.

Another supporter is Rep. Alexandria Ocasio-Cortez of New York, another top leader of the left in the House.

She took to Twitter after the town hall to emphasize that "we've got the *Senate Majority Leader* on board to forgive $50k. Biden’s holding back, but many of the arguments against it just don’t hold water on close inspection. We can and should do it. Keep pushing!"

Biden has called for forgiving $10,000 in student loan debt as part of a larger coronavirus relief effort. He also extended a freeze on student loan payments through Sept. 30, 2021, immediately upon entering office last month.

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The president also forcefully reiterated his longstanding opposition to defunding the police, which has been the aim of many on the left since last spring and summer's nationwide racial protests and unrest over police brutality against minorities.

Asked during the town hall about how not to "over-legislate" police officers, the president outlined the steps he hopes to take to improve criminal justice and policing in the country.

"By number one, not defunding the police," Biden emphasized. "We have to put more money into police work so that we have legitimate community policing and we are in a situation where we change the legislation."

In the wake of the death of unarmed Black man George Floyd last May while in the custody of police officers in Minneapolis, Minn., some Democrats have pushed to diverting funding for local police budgets to social and mental health services.

Since last summer, Biden’s opposed calls to defund the police. On the presidential campaign trail, the then-Democratic nominee promised to invest $300 million for police training and the hiring of more diverse officers.

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The third comment from the town hall that is anything but music to progressives' ears was the president’s call to "gradually" raise the minimum wage to $15 per hour.

Biden suggested that he could be open to a longer phase to boost the minimum wage than what's currently spelled out in the congressional Democrats' bill. He reiterated his backing for a $15-per-hour minimum wage, saying "I do support a $15 minimum wage. …no one should work 40 hours a week and live in poverty."

But he added that "it's totally legitimate for small-business owners to be concerned about how that changes."

The president's previously suggested that the minimum wage boost may not make it into the final version of the massive $1.9 trillion coronavirus relief bill, but his comments – coming in prime time on a national cable news network – grabbed plenty of attention.

The current federal minimum wage is $7.25 per hour and raising it has long been the goal of progressives.

Sen. Bernie Sanders of Vermont – the progressive champion and two-time Democratic presidential contender – has vowed that the final version of the COVID relief bill will include language on raising the minimum wage to $15 per hour.

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Sanders took to Twitter on Wednesday morning to write that "The overwhelming majority of the American people understand that we must end starvation wages in America. That means raising the minimum wage from $7.25 an hour to $15 an hour by 2025. Period."