Cedar Rapids, Iowa (CNN) Joe Biden has visited Iowa countless times over 32 years, in previous presidential bids and as vice president. But Tuesday was the first time he arrived in the state as the Democratic front-runner .

And in his first stops in eastern Iowa, Biden acted as if he was already in a general election match-up with President Donald Trump.

In the first minutes of a rally in Cedar Rapids, he again lambasted Trump over the 2017 rally in Charlottesville, Virginia, organized by white supremacists -- where Trump responded to the killing of a counter-protester by claiming there had been "very fine people on both sides."

Biden mocked Trump for defending those words last week, saying he had "doubled down on concocting a phony story on how these violent thugs only wanted to protect" the city's statue of Confederate Gen. Robert E. Lee.

"Enough's enough, man. This is nonsense. The very rally was advertised -- advertised -- as a white supremacist rally," Biden said.

He accused Trump of waking up each day eager to "wage war on Twitter."

"Everybody knows who Donald Trump is," he said. "I want to make sure they know who we are -- who I am."

Though he swung repeatedly at Trump, Biden pulled his punches when it came to other Democratic contenders. He deflected questions about Vermont Sen. Bernie Sanders' criticism of his votes for the Iraq war and the North American Free Trade Agreement — and signaled he would not be engaging with his primary foes anytime soon, saying there will be "plenty of time on stage" once the party's presidential debates begin in late June.

"I'm not going to get in a debate with my colleagues here," he told reporters during a stop at an ice cream shop in Monticello.

"They talk about, there's a division in the Democratic Party," Biden said later on Tuesday night in Dubuque. But, he added, "we agree on basically everything, all of us running -- all 400 of us."

The early days of Biden's presidential bid have been marked by Trump ignoring his advisers' urges and repeatedly attacking Biden in front of reporters and on Twitter -- and Biden responding.

The contrast has played perfectly into Biden's hands: One driving force behind his candidacy is a sense among Democratic primary voters that he would stand a better chance of defeating Trump in 2020 than the party's lesser-known and more progressive candidates.

National polls on Tuesday found that Biden's entrance had helped him surge into the high-30s among Democratic voters -- making him the clear front-runner with more than double the support of his two nearest opponents, Sanders and Massachusetts Sen. Elizabeth Warren, who has also seen her support grow in recent days.

In Cedar Rapids, Janet Leonard, a retired teacher who lives in Manchester, said she backed Biden in the 2008 Democratic caucus and will again because she sees him as having the best shot at ousting Trump.

"Joe can not only get the Democrats, but the independents and even the Republicans who maybe voted for Trump but are not really happy," she said. "I think he is the most electable candidate. No matter what, we have to get somebody who is going to beat Trump."

Biden is also leaning heavily on one tool he has that no other Democrat can match: being former President Barack Obama's vice president.

His campaign released a video Tuesday morning that featured Obama praising Biden in 2017 -- even though Obama does not plan to endorse a candidate during the Democratic primary. Then, in Cedar Rapids, Biden called Obama an "extraordinary man."

"He was a president our kids could look up to," Biden said.

An air of nostalgia hung over a basement room in Cedar Rapids, where several supporters came wearing blue and white "Biden" T-shirts from his 2008 campaign.

Biden promised in what was his first stop as a 2020 candidate in Iowa that voters would "see a heck of a lot of me," and that "no one's going to work harder" to earn Democratic caucus-goers' votes.

Biden has so far kept his stump speeches relatively short and trimmed them of his past references to former Republican colleagues he liked and worked with. He has also left out policy positions that could be fodder for Democratic criticism, such as his support for free trade.

Instead, Biden has touted an agenda that includes undoing Trump's tax breaks, increasing the minimum wage to $15 an hour and "making sure we finish the job on health care" by creating a public option that would allow anyone to buy into Medicare.

Pete Wernimont of Cedar Rapids, a longtime admirer of Biden, brought a copy of the former vice president's book, "Promise Me, Dad" for an autograph. As he walked away from the rally, he said he was nearly entirely sold on Biden's candidacy.

"I'm about 80 to 90% there," he said, adding that he was also intrigued by South Bend, Indiana, Mayor Pete Buttigieg.

For now, though, he believes Biden is the most electable Democrat in the race.

"Trump's going to have a real fight on his hands," Wernimont said. "I believe Biden can beat him."

Kerry Robertson, a retired veteran, showed up at the Veterans Memorial Building in downtown Cedar Rapids not realizing that his weekly card game with friends had been replaced by a Biden campaign stop. Robertson, who says he didn't like Trump or Hillary Clinton and instead voted for an independent -- he can't remember which one -- in 2016, said Biden had earned his support.

"If he can do something to keep Social Security and Medicare and Medicaid, that's what a hell of a lot of people depend on, you know?" he said.