Westerville, Ohio (CNN) If anyone had doubts that Elizabeth Warren has seized the mantle as the new front-runner in the Democratic field, they were laid to rest on Tuesday night as she became the target of almost every rival on the debate stage -- fending off attacks on everything from the leftist bent of her ideas to whether she is capable of a yes-or-no answer on taxes.

It was a rough-and-tumble welcome in the arena for a candidate who has gamely sidestepped attacks in previous debates. But at the CNN/New York Times debate Tuesday night in the crucial swing state of Ohio, the Massachusetts senator was constantly on defense driving her central argument that Democrats must "dream big" and "fight hard." All the fire sent in Warren's direction at Otterbein University underscored a marked shift in the Democratic race that has been underway for many weeks: while former Vice President Joe Biden has remained strong in the polls, the other candidates in the race clearly now see Warren as the real competition.

It was one of the first times Warren had to face a barrage of critiques from her Democratic competitors, navigating many of the critical comments usually aimed toward Biden or Sen. Bernie Sanders of Vermont.

It was the moderates in the race who targeted the newly minted front-runner the most. South Bend, Indiana, Mayor Pete Buttigieg set that aggressive tone from the opening moments of the debate as he sought to seize the centrist lane within the Democratic field. Challenging Warren on her refusal to answer a yes-or-no questions about whether her plan would lead to tax hikes from the middle class, he said her evasiveness embodied the very reason why Americans are so frustrated with Washington.

"Your signature is to have a plan for everything, except this," Buttigieg said to Warren. "No plan has been laid out to explain how a multi-trillion dollar hole in this plan that Sen. Warren is putting forward is supposed to get filled in."

In a strong performance, Buttigieg repeatedly argued that Democrats would not be able to sell some of Warren's more liberal ideas -- namely "Medicare for All" -- to the broader universe of voters that the party must sway to win the White House.

"I don't understand why you believe the only way to deliver affordable coverage is to obliterate private plans," Buttigieg said to Warren. "We're competing to be president for the day after Trump. Our country will be polarized, more than now. After everything we have been through, after everything we are about to go through, this country will be more divided. Why divide this country over health care when there's a better way to deliver coverage for all?"

Warren did not back down, but at times seemed surprised by the force of the attacks against her -- even from the normally mild-mannered former Texas Rep. Beto O'Rourke who accused her of embracing a philosophy that was punitive.

"Look, I understand that this is hard, but I think as Democrats we are going to succeed when we dream big and fight hard, not when we dream small and quit before we get started," she said.

Buttigieg's arguments were often amplified by Minnesota Sen. Amy Klobuchar, who also leaned heavily on her Midwestern roots to argue that Warren and Sanders have driven the party too far to the left. In one tense exchange, the Minnesota senator referred to "Medicare for All" -- a proposal that was crafted by Sanders and endorsed by Warren -- as a "pipe-dream."

"The difference between a plan and a pipe dream is something that you can actually get done," Klobuchar said.

"At least Bernie is being honest here and saying how he's going to pay for this -- and that taxes are going to go up," she added. "We owe it to the American people to tell them where we will send the invoice."

At another point Warren was repeatedly badgered by California Sen. Kamala Harris, who tried to force her into agreeing with Harris's proposal that Trump should be thrown off Twitter. It was then that Warren showed a touch of exasperation.

"Look, I don't just want to push Donald Trump off Twitter, I want to push him out of the White House," Warren said.

Biden touts record, Sanders thanks well-wishers

While he often receded into the background on Tuesday night, Biden argued that he had done bigger things than anyone else on stage, citing the Violence Against Women Act as one example.

Though he did not take on Warren as aggressively as some of the others, he tried at one point to take credit for getting the votes in Congress to make her idea for the Consumer Financial Protection Bureau a reality. "I got votes for that bill," Biden said, referring to the 2010 Dodd-Frank Act that established the bureau. "I convinced people to vote for it, so let's get those things straight too," he said.

Pushing back on that idea, Warren offered her thanks to Biden's then-boss, President Barack Obama and everyone else who helped create the agency -- pointedly not mentioning the former vice president.

"I am deeply grateful to President Obama, who fought so hard to make sure that agency was passed into law," Warren said.

Biden, grinning as he stood beside her, graciously offered a compliment: "You did a hell of a job in your job," he said to her.

"Thank you," she replied.

When the conversation turned to the age of the three leading candidates -- Biden, Sanders and Warren -- who are all in their 70s, Biden also sought to frame his age as an asset. He promised to release his health records, along with some two decades of his tax information.

"Look, one of the reasons I'm running is because of my age and my experience," Biden said. "With it comes wisdom. We need someone to take office this time around who on day one can stand on the world stage, command the respect of world leaders from Putin to our allies, and know exactly what has to be done to get this country back on track."

Sanders, who was back on the trail for the first time since his heart attack, tried to allay any concerns about his stamina by stating that he's "healthy" and "feeling great." The 78-year-old also offered his thanks for the well wishes he has received over the past two weeks.

"Let me take this moment if I might to thank so many people from all over this country, including many of my colleagues up here, for their love, for their prayers, for their well wishes," he said. "And I just want to thank you from the bottom of my heart, and I'm so happy to be back here with you this evening."

Gabbard spars with Buttigieg

Facing the Democratic Party's increasingly difficult threshold to make the next debate in Georgia, some of the lower tier candidates clearly knew that they needed to generate a jolt of energy for their campaigns on Tuesday night. But the only candidate at that level who drew notice was Rep. Tulsi Gabbard of Hawaii.

Gabbard, an Iraq War veteran who served in the Army, has called for US troops to leave Syria and she sparred with Buttigieg -- the only other veteran on the stage -- over US engagement in that conflict.

The Hawaii congresswoman criticized Trump's sudden decision to abandon Kurdish forces near the northern Syrian border -- a move that essentially opened the door for a Turkish military offensive against the longtime US allies. She described the "slaughter of Kurds" by Turkey as a consequence of "the regime-change war that we've been waging in Syria."

"Donald Trump has the blood of the Kurds on his hands -- but so do many of the politicians in our country from both parties who have supported this ongoing regime-change war in Syria that started in 2011," Gabbard said, "along with many in the mainstream media, who have been championing and cheerleading this regime-change war."

Buttigieg, who served in the Navy Reserve, told Gabbard she was "dead wrong."

"The slaughter going on in Syria is not a consequence of American presence, it a consequence of a withdrawal and a betrayal by this President of American allies and American values," Buttigieg said.

He noted that he did not support going into Iraq and believes that the US should get out of Afghanistan, but said it was also the case that "a small number of specialized, special operations forces and intelligence capabilities were the only thing that stood between that part of Syria and what we're seeing now, which is the beginning of a genocide and the resurgence of ISIS."

"When I was deployed I knew one of the things keeping me safe was the flag on my shoulder represented a country that kept its word," Buttigieg said. "You take that away, it takes away what makes America America."