Analysis by Ronald Brownstein with data analysis by Aaron Kessler, CNN

(CNN) -- Support for a government takeover of health care is Exhibit A in the charge by President Donald Trump and other Republicans that the Democratic majority in the House of Representatives has lurched to the left.

But a close examination of sponsorship for the House legislation recently introduced by Rep. Pramila Jayapal of Washington state to establish a single-payer government-run health care system shows instead the obstacles that progressives still face in fundamentally redirecting the party.

Though the single-payer idea is generating much more conversation than previously from prominent Democrats -- including endorsements from several candidates seeking the party's 2020 presidential nomination -- it has attracted very little support from House members beyond the most reliably Democratic districts, a CNN analysis has found. Unless and until the idea wins more House Democrats who represent swing districts that voted in 2016 for Trump, or even backed Hillary Clinton only narrowly, it cannot approach the 218 votes needed for passage. The same pattern -- and challenge -- is evident to an even greater extent on the Green New Deal resolution introduced by first-term Rep. Alexandria Ocasio-Cortez of New York.

Which Democrats support single payer health care

The single-payer bill introduced last week by Jayapal has 104 cosponsors among voting members of the House. (Two nonvoting delegates, from Washington, DC, and the Northern Mariana Islands, have also cosponsored the bill). Though Jayapal says the supporters expect to add more cosponsors, that list is currently down from the 124 who backed similar legislation from Rep. John Conyers of Michigan in the last Congress.

To assess the pattern of support for the single-payer idea, CNN producer Aaron Kessler compared those who have, and have not, cosponsored the bill through a database tracking the political and demographic characteristics of all 435 House districts. That analysis shows that the 105 voting Democrats supporting the single-payer bill this year present a distinct profile.

The vast majority, 103 of the supporters, represent districts that voted for Clinton over Trump in 2016. Just two of the cosponsors -- Rep. Matthew Cartwright in Pennsylvania and first-term Rep. Jared Golden of Maine -- hold seats that backed Trump in 2016. Only four more cosponsors represent competitive districts that Clinton carried narrowly over Trump: Josh Harder in California, Jahana Hayes in Connecticut, Tim Ryan of Ohio and Susan Wild of Pennsylvania represent Clinton-won districts where Trump attracted at least 44 percent of the vote.

Put another way, the cosponsors represent just over half of all the House Democrats holding districts that Clinton carried (103 of 204 in total). But they constitute fewer than 1 in 4 of those in Clinton-won districts where Trump captured at least 44% (four of 18.) And the cosponsors represent only about 1 in 16 of the Democrats from districts Trump carried (two of 31).

The same imbalance is evident when looking at seats that Democrats flipped from Republican control last fall. Of the cosponsors, just seven represent districts that Democrats won from the GOP in 2018. That's only about one-sixth of the 43 Democrats in all holding such seats in the House. (Four of the seven cosponsors in flipped seats are from California: Katie Porter, Katie Hill and Mike Levin, all in Southern California, and Harder, from the Central Valley.) By contrast, 98 of the sponsors represent districts that Democrats controlled before November. That's just over half of all the Democrats in such seats.

Support is more intense than broad

The pattern is very similar on the resolution from Ocasio-Cortez to create a Green New Deal. Support for that idea so far is limited even more narrowly to Democrats who hold the party's safest House seats, the analysis found.

Counting Ocasio-Cortez, 88 voting House Democrats have endorsed the plan. All of them except Sean Maloney in New York's Hudson River Valley hold seats in districts that voted for Clinton over Trump; just four are in Clinton-won districts where Trump carried even 44% of the vote. Only two hold seats that flipped from Republican to Democratic control last fall: Levin, whose district straddles Orange County and San Diego in Southern California, and Debbie Mucarsel-Powell, who won a Miami-area seat.

The patterns of support for both single-payer health care and the Green New Deal point toward the new fault lines likely to shape the legislation that emerges from the Democratic-controlled House over the next two years.

While social issues such as gun control formerly created the most imposing divisions among Democrats, the party is achieving much greater unity on those issues as it has shed members from culturally conservative rural districts and built a different majority centered on socially liberal urban and suburban seats. The biggest divides now may come around economic questions, particularly taxes, spending and the role of the federal government.

The ambitious proposals on health care and climate change may reveal more about the intensity than the breadth of liberal perspectives in the new House majority. Gary C. Jacobson, a University of California at San Diego political scientist who specializes in Congress, says proposals like those for a single-payer health care system and the Green New Deal reflect the genuinely growing demand in strongly Democratic areas "that they do something to counteract Trump." But that doesn't mean a wider range of Democrats than in the past can safely support such ideas, he argues. "Their majority rests on people from centrist and Republican-leaning districts," Jacobson says, and those members cannot embrace these proposals "unless they are suicidal."

Neil Sroka, communications director for Democracy for America, a liberal group that has described the Jayapal bill as "the gold standard" in single-payer legislation, says it's not surprising that the legislation's initial support tilts toward members from "bright blue Democratic districts." Sroka agrees that advocates must expand support for the idea among Democrats from more contested terrain, but he argues the key to that is creating a more visible national debate around the issue -- preferably behind a 2020 Democratic presidential nominee advocating the idea.

"The key is having a robust national discussion about the failures of our current health care system and what Democrats imagine is necessary to make it better," Sroka says. "And the easiest way to do that is having a nominee who supports a robust plan of Medicare-for-all."

But centrists skeptical of single-payer health care and the Green New Deal say more discussion isn't likely to erode the skepticism among Democratic members from more closely contested districts. In a study, the centrist Democratic group Third Way found that just two of the 92 Democrats in the most competitive House races last year ran ads endorsing Medicare-for-all, and both of those candidates lost.

"None of the people that were able to win in tough districts in 2018 ran on Medicare-for-all, and the reason is that they can't," says Matt Bennett, Third Way's executive vice president for public affairs. "People in those districts don't support it."

The political verdict may not be quite so absolute: the seven Medicare-forall cosponsors who flipped Republican House seats last fall did not hide their support for the idea, even if they did not necessarily broadcast it in television ads. Still it remains true that, at this point, the Democratic House "majority is built by people who are not on those bills," as Bennett puts it.

Jacobson similarly says the core problem facing progressives is that there are not 218 House districts liberal enough that lawmakers could safely endorse these ideas. "Liberals are always going to have to compromise with centrists if they are going to be a majority at all," he argues.

Other divides among Democrats

Two other imbalances in the pattern of support for the single-payer bill are also revealing, though less lopsided than the contrasts along lines of political allegiance. Fifty-two of the cosponsors are from districts where the median income is below the national average: that represents just over half of the 99 Democrats holding such seats. But after the party's sweeping suburban gains last fall, Democrats represent a growing number of affluent suburban districts, and support for single-payer is more restrained among members from such places.

Of the 136 Democrats representing districts where the median income exceeds the national average, a considerably smaller share, slightly below two-fifths, have endorsed the bill. The contrast is similar on diversity: While just under half of the 144 Democrats in seats with more minorities than the national average have endorsed the bill, slightly less than two-fifths of those in seats that have more whites than average have joined them.

In contrast to the Medicare-for-all bill, support for the Green New Deal leans slightly upscale: 58 of the 88 cosponsors are from districts in which the median income exceeds the national average. That may reflect the appeal of environmentalism in relatively affluent suburbs.

But the bigger story may be the overlap of support and opposition to both measures. Sixty-four House Democrats have cosponsored both the Medicare-for-all legislation and the Green New Deal resolution. Another 65 have sponsored one of them, but not the other. That means fully 106 of the 235 House Democrats have not sponsored either proposal at this point.

Sroka says House support for single-payer health care, in particular, will broaden if the Democrats' 2020 nominee runs on it and proves it can turn out more irregular voters. That could increase the tolerance for a vanguard liberal agenda even in districts that now are closely divided between the parties or leaned toward Trump in 2016, he argues. "Part of the way you build support among these swing districts is by actually helping to change the electorate," he says.

But Bennett says it's wishful thinking to assume that Democrats can reconfigure the electorate so decisively in 2020 that they no longer need to worry about moving too far left to hold conflicted voters in swing districts and states. Persuading those swing voters, he maintains, will be critical to Democratic hopes of both holding the House and ousting Trump. "That requires us," he says, "to address people's kitchen table concerns in those places in ways that make sense to them, that sound like it's going to happen in their lifetime, and not engage in faculty lounge debates about what the optimal solution is."