Joe Biden and Pete Buttigieg are considered the leading 2020 Democratic moderates, but even they have taken positions to the left of Barack Obama — illuminating the liberal drift of the entire party. Why it matters: In earlier cycles, both men would have been labeled liberals based on their platforms and biographies. The fact that they're called centrists now in the media shows how much the Democratic Party has shifted in a polarized era — just as the Republican Party has been reinvented under President Trump.The big picture: "The center in American politics shifts in every era," Matt Bennett, co-founder of the center-left think tank Third Way, told Axios. "The world changes, and so do our politics."As FiveThirtyEight has reported, data from the General Social Survey suggests that Democrats have moved left on a variety of issues — health care to some extent, but particularly on race and immigration.Gallup found that Americans self-identifying as "liberal" rose from 17% in 1992 to 26% in 2018, offsetting the decline of "moderate" while "conservative" stayed about the same.But, but, but: Trump's campaign advisers say Democrats' leftward pull works to his advantage in swing states.Trump's campaign will affix the “socialist” label to Biden or Buttigieg if either emerge as the Democratic nominee, communications director Tim Murtaugh tells Axios' Jonathan Swan. “There is no centrist lane." Trump's message would include criticisms that Biden or Buttigieg would abandon voters who are employed by or rely on the fossil-fuel industry; support taxpayer-funded abortions; expand government's role in health care; and give undocumented immigrants free health care.Andy Surabian, a Republican strategist close to the Trump campaign, foreshadowed Trump surrogates' message to Swan: "The only thing moderate about Biden or Buttigieg is their branding."Between the lines: Here are some of the Biden and Buttigieg positions that are being called centrist today, but would have been liberal dreams during the Bill Clinton years and still out of reach in the Obama era:Health care: Democrats’ appetite for government-run health insurance has steadily increased as the party has moved left and the health care system has gotten more precarious, per Axios' Sam Baker.Clinton’s failed health care overhaul would have relied entirely on private insurance, with tight federal regulations.Obama’s Affordable Care Act created a new market for private plans, but it relied just as heavily on an expansion of Medicaid — an existing government program. He also wanted to create a new public plan that would compete with private insurers, but moderate Democrats deemed it too liberal and killed it.Biden and Buttigieg not only want a public option, but are pushing more aggressive versions than what Obama endorsed. Obama’s public option only would have been available to a relatively small slice of the population, but Biden and Buttigieg would make theirs open to anyone. Climate change: Biden and Buttigieg support the Green New Deal, though they've also released climate change frameworks of their own. Neither Obama nor Clinton supported anything as sweeping as the Green New Deal.Budgets: Clinton wanted to balance the national budget, while Obama took a milder swing at deficit reduction. Biden and Buttigieg rarely talk about budgets or spending, except to knock the Medicare for All plans championed by Bernie Sanders and Elizabeth Warren.College: Both Biden and Buttigieg support some form of free college — something that was never on the Clinton or Obama agendas. Biden’s proposal includes free community college, while Buttigieg’s plan calls for free public colleges and universities for families making less than $100,000 per year.LGBTQ rights: Clinton signed the Defense of Marriage Act federally defining marriage as between a man and woman. Obama initially opposed gay marriage, until "evolving" in 2012 — after Biden came out in support of it.Biden has said the Equality Act — which would address discriminatory practices against LGBTQ Americans — would be his top legislative priority if elected president.Buttigieg, a military veteran who is gay and is married, has an 18-page plan that includes rolling back the Trump-era policy that prohibits insurance coverage for gender reassignment surgeries for military veterans. He's also proposed adding a non-binary gender option on various federal forms and documents, like passports.The bottom line: "This is the legacy of polarization," Darrell West, vice president and director of Governance Studies at Brookings, told Axios."Republicans are embracing much more conservative ideas than they've ever had, and Democrats are embracing more liberal ideas than they have in the past."