(CNN) Three congressman who currently sit at the bottom of the polls sought to start their climbs in a crowded Democratic presidential field during a trio of CNN town halls Sunday night.

All three pushed back against some of the most aggressively progressive programs being pushed by fellow Democratic contenders like Sens. Bernie Sanders and Elizabeth Warren. Instead, they saved their sharpest words for President Donald Trump, with Ryan announcing he would back a start to impeachment proceedings.

They were also united in their support for stricter gun regulations and, in more modest strokes, efforts to guarantee health care beyond Obamacare -- with each saying they would push for a "public option" allowing people to buy into Medicare.

Here are 9 takeaways from Sunday night's town halls:

Moulton: Presidents shouldn't be protected from indictment

Moulton said he would seek to change current Justice Department guidelines that say a sitting president cannot be indicted.

He also said he backed a start to impeachment proceedings against Trump -- even if meant some political blowback.

"I understand that the politics might be tricky, OK?" Moulton said. "But how about just doing the right thing. You know? How about doing the right thing? Because I swore an oath to protect the Constitution."

A new CNN poll this weekend found that support for impeachment is inching up, to 41% from 37% in late April. That movement, though, was fueled by Democrats. Seventy-six percent favor it now, up from 69% in April.

Moulton on America's 'problem with racism'

Moulton said the country's ongoing "problem with racism" prevented Democrat Stacey Abrams from being elected governor of Georgia in 2018.

"If this country wasn't racist, Stacey Abrams would be governor," Moulton said on Sunday night. "Because people of color are being systemically denied the most basic right in a democracy, which is the right to vote."

Moulton's comment came after a question about combating systemic racism. He said the United States needs a "new Voting Rights Act" -- a reference to Democratic objections to measures imposed by GOP-led states that have limited early voting, imposed strict voter ID laws and more.

Georgia Gov. Brian Kemp, who narrowly defeated Abrams last year, previously served as secretary of state and his administration came under fire for taking controversial steps to, as Abrams and civil rights groups alleged, suppress the minority vote.

Pushback against Medicare for all

Moulton warned against pushing forward for a Medicare for all, single-payer program, instead -- like many other moderate Democrats -- suggesting a "public option" that would allow Americans to buy into a program like existing Medicare.

He said his skepticism over " Medicare for all " is rooted in his experience with the Department of Veterans Affairs, which uses a form of single-payer health care.

"I've seen the good, the bad and the ugly," Moulton, an Iraq war vet, said of his time on a health plan through the VA.

He praised the system for its ability to negotiate and lower prescription drug prices, but also talked about veterans on waiting lists for care.

Moulton said he preferred "what President Obama planned (in the run-up to the passage of the Affordable Care Act), which is that we should have a public option like Medicare for all" -- arguing that Americans should be able to buy in to a modernized version of today's Medicare program.

The Medicare for all bills in the House and Senate would not expand Medicare as most Americans know it, but would create a new single-payer system that would effectively wipe out private insurance.

Ryan backs impeachment after Mueller's comments

Ryan, who has previously been more cautious to call for impeachment proceedings, on Sunday said he now believes it's time to start the process against Trump.

He cited former special counsel Robert Mueller's remarks last week in pushing him to support congressional action, saying he wanted to know from Mueller whether it was only Trump's status as president that prevented Mueller from charging him with crimes.

"I wanted to know that answer," Ryan said, "and the answer I got a couple days ago was yes, he would have."

Ryan also explained why he had been so cautious even as the evidence turned up by Mueller had become public.

"I know what (impeachment) is going to do to the country," he said. "I take no joy in this, at all. But I have a duty and responsibility and that duty and responsibility is led me to think we have to do this."

Ryan not comfortable with all-white, all-male 2020 ticket

Asked if he'd be comfortable with an all-white, all-male Democratic 2020 ticket, Ryan said "no, absolutely not."

"Our ticket and the next president's cabinet must reflect the diversity of the country. And I'm committed to do that," said Ryan, who is himself a white man.

Ryan pointed to Youngstown, Ohio, being 50% African-American, and said his focus on economic policies would direct investment toward struggling areas.

"White, black, brown, gay, straight, I will be a working-class president for the American people," he said.

Ryan criticizes Trump's China tariffs

Ryan has long supported restrictions on free trade, but on Sunday he lambasted President Donald Trump for imposing tariffs that are "not targeted" on imports from China, saying that "we have no clue what the plan is, what the strategy is, and our farmers are getting hammered."

"Trump does not have a big strategy. He has a tactic that gets him on TV because he sends a tweet out -- tariffs are on, tariffs are off -- and the media runs with it all the time and it changes the subject and he can look tough," he said. "We're getting our clock cleaned."

Ryan predicted that the top issue confronting the next president is the United States' relationship with China.

Swalwell vs. Sanders

Swalwell split with the Democratic left on two major proposals headed up by Sen. Bernie Sanders.

The California congressman said he did not agree with Sanders' proposal to extend voting rights to people currently in prison. He does support returning the right to most people after they serve their sentences.

"I do not believe that the Boston marathon bomber or the last person I prosecuted, who shot a 17-year-old a week before he was to graduate" should be able to vote right now, Swalwell said. When posed a similar question at a CNN town hall in April and on other occasions, Sanders has argued that stripping any American of their voting rights, no matter the cause, creates a slippery slope that plays into the hands of Republican governors who have sought to restrict the franchise with laws like voter ID.

Swalwell also broke from the party's left by hedging on the implementation of Medicare for all as the legislation is currently written, saying he agrees with "90%" of the bill but thinks people should be allowed to choose private insurance.

"I think ingrained in our DNA is choice. People want to have choices, but they also expect that the government should offer an affordable plan if their employer is providing it," Swalwell said, adding that his plan would offer options as well as negotiate prescription drug costs.

Sanders' bill would effectively eliminate private insurance.

Student loan debt hits home for Swalwell

The 38-year-old congressman said on Sunday night that he's still paying off what was $100,000 in student loan debt.

"The way I see it is that the lessons and memories of college should last a lifetime," he said. "The debt should not."

The burden is "deferring the dreams of our generation," he added, noting his support for making community college free and saying he has a plan to make college debt-free in part by bringing down the interest loan to zero on student loans.

"If you do work study all four years through, you learn and you earn, and then you come out and you take your first job and do volunteer service for communities that need it, it's debt-free education. College should work for you if you work for college in America," Swalwell said.

Swalwell's plan stops short of the most ambitious one in the field, from Sen. Elizabeth Warren, who has proposed a one-time forgiveness plan that would eliminate nearly $650 billion in outstanding student debt.

No impeachment push -- yet -- for Swalwell

Swalwell did not follow Ryan's lead in calling for a start to impeachment proceedings against Trump.

The issue has divided the Democratic House caucus and the 2020 candidates, even as more of them have shifted in its favor following former special counsel Robert Mueller's press conference last week.

Still, Swalwell was careful not to rule out the possibility and -- like House Speaker Nancy Pelosi has urged -- said he wanted to know more before going forward.

"If that's where we're headed, I want to be backed into it," Swalwell said, "showing that we've exhausted every other remedy and have the American people with us. I think that's where we are right now."

He was less circumspect when it came to the fates of Trump's Treasury Secretary Steven Mnuchin and Attorney General William Barr, suggesting House Democrats should first "make an example" out of the pair.

"I think you have to make an example out of Mnuchin and Barr first, though," he said. "You can't let them off the hook."

Barr's initial summary of Mueller's findings, and his subsequent defenses of Trump, have angered Democrats who believe he is acting more like a surrogate for the President than an independent actor loyal first to the law.