DETROIT — There were two nights of debate this week among the Democratic presidential candidates but only one winner: Elizabeth Warren.

A flurry of polls in the coming days will show the numbers for the 20 contenders nudged temporarily up or down as a result of how they performed here, but no one did a better job than the Massachusetts senator in laying out a purpose for seeking the presidency and offering a clear picture of what she will do with it if she wins.

The most memorable line of either night was Warren’s brush-back of rival John Delaney’s suggestion that she was running on “impossible promises.”

“I don’t understand why anybody goes to all the trouble of running for president of the United States just to talk about what we really can’t do and shouldn’t fight for,” Warren answered.

Her presence lingered on the stage of the Fox Theatre on Wednesday — so much that former vice president Joe Biden was asked to respond to her declaration the night before that “spinelessness” would not solve the nation’s big problems.

Biden’s answer was not to look forward, but backward, at the Obama administration’s efforts to revive the economy a decade ago in the wake of the financial collapse.

Where Warren offers a vision for her candidacy and frames it in a compelling way, Biden has a rationale: the increasingly fragile supposition that he is the most electable candidate in the field.

That has been enough to put him at the top of the polls — and keep him there thus far. But the more opportunities people have to see him as an actual candidate, the sharper the contrast against what they had assumed about him.

Biden was not as shaky Wednesday night as he had been during the first debate in Miami, but the improvement was a modest one, as he continued to wrap himself in gauzy nostalgia for the Obama presidency.

The limitations of running on a record of being someone else’s wingman quickly became apparent.

New York Mayor Bill de Blasio pressed Biden on his refusal to say whether he had urged President Barack Obama to change his administration’s policy on deportations: “You want to be president of the United States, you need to be able to answer the tough questions. I guarantee you if you’re debating Donald Trump, he’s not going to let you off the hook. So did you say those deportations were a good idea, or did you go to the president and say this is a mistake, we shouldn’t do it. Which one?”

Sen. Cory Booker (D-N.J.), who had a good night, piled on: “You can’t have it both ways. You invoke President Obama more than anybody in this campaign. You can’t do it when it’s convenient and then dodge it when it’s not.”

While selecting a candidate most likely to beat President Trump next year is the Democrats’ top priority, a party’s primary is also an exercise that defines its direction and its identity. We need look no further back than the 2016 Republican contest to see how sharp the turn can be.

As much as they revere Obama, Democrats do not — and should not — see his presidency as an end point. The challenge for them now is figuring out which of his achievements they want to build upon and where they want to make a course correction.

Warren has significant vulnerabilities. If you believe the polls, her policies on health care and other issues go further to the left than the market will bear. But by keeping her message focused on the how she would solve the nation’s challenges and how she would shake up the existing order, she is offering a model that the other candidates, especially Biden, would do well to emulate.

There is room to do this from the center. It is possible to put forward a moderate, forward-looking vision that is also muscular and clear. Bill Clinton did it in the early 1990s, albeit in a moment that was very different than this one.

But coming out of the second round of debates, the race remains a muddle. Part of the problem is the size of the field, which requires the party to split these showdowns into two nights. That will change, possibly as soon as next month.

And Biden and Warren have yet to share the stage. When that finally happens, it may well turn out to be the clarifying moment Democrats are looking for. The time for squabbling about the past will be over, and the one for making choices about the future will have arrived.

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