Democrats are chasing two contradictory impulses in their quest to defeat President Trump: Move past Barack Obama's policies, but tap into the party's affection for him. Why it matters: It's hard to watch a Democratic debate without being reminded of Obama's legacy. "We have to rebuild the Obama coalition," Sen. Kamala Harris said at Wednesday's debate, a point that was echoed by other candidates. "I keep referring to that because that's the last time we won."The big picture: 2020 Democrats' evolution on health care is the most obvious example of how far the party has moved on policy since the Obama years. It's not just the push for Medicare for All by Sens. Elizabeth Warren and Bernie Sanders. Calls for a public option or something like Pete Buttigieg's "Medicare for All Who Want It" are still a change from the politics of 2009-10, when Democrats couldn't get a public option or single-payer plan passed.Universal health care with a public option was the liberal extreme a few years ago; in 2020 it's the moderates' lane. "I think it is important for candidates to push past what I was able to achieve as president," Obama said during a speech last week, admitting himself that it's time to move past the policies of his tenure. "I don't want people to just revert to what's safe; I want them to push out and try more."At the same time, Obama warned not to stray too far from what a consensus of Americans are willing to support. "I think it is very important for all the candidates who are running at every level to pay some attention to where voters actually are."Climate is another big example of Democrats' post-Obama positioning. Nearly all Democratic candidates are espousing more aggressive, progressive climate policies and goals, per Axios' Amy Harder:Banning fracking, and overall fossil fuel development, on federal lands. Obama had never proposed banning it, and even supported it early on his presidency. Pushing mandates over market-based policies like cap-and-trade, which was the type of legislation Obama tried to get through Congress early in his presidency.Cutting emissions to zero within 30 years, compared to 80% by that time, which was Obama's goal when he left office. "Now we have an opportunity to move that [Obama] ship much further and much faster toward progress," said Adam Green, founder of the Progressive Change Campaign Committee.Immigration was a big part of the first Democratic debate discussion and showed how 2020 Democrats are re-examining Obama's legacy.Harris took issue with an Obama-era deportation program, several candidates said they'd support providing health care to undocumented immigrants, and Julián Castro took aim at Joe Biden for not reckoning with the number of deportations that occurred during the Obama administration. Foreign policy is one of the least defined and discussed areas so far inside the Democratic presidential contest. But some trends have emerged, per Axios' Dave Lawler.On China, including trade, much of the field has moved toward a more hawkish position than Obama — with China being discussed more as a threat than as a potential partner.On Israel and Saudi Arabia, meanwhile, much of the Democratic field has been more openly critical than Obama. Democrats advocate for a return to Obama's approach on Iran over Trump's, and long for a time when the U.S.got along with its allies better than its adversaries such as Kim Jong Un or Vladimir Putin.At the same time, Democrats on the trail are not wholeheartedly embracing Obama's approaches on unresolved conflicts that drew mixed reviews under Obama, such as Syria. The bottom line: While 2020 Democrats aren't shy about moving away from Obama's policies, we've seen their embrace of Obama-era political leadership and rhetoric — because they want to keep the spirit of the last Democrat to win the White House."Instead of talking about the Obama coalition, it might be worth talking about what President Obama achieved, which is a high degree of unity among different kinds of people and a vision which people in Iowa saw themselves in as much as people in Los Angeles or Baltimore or Michigan," said Cecilia Muñoz, who headed Obama's White House Domestic Policy Council.