That’s even though a majority of Americans, including most Republicans, say Trump does not represent the Republican Party’s core values, and six in 10 overall – including three in 10 in his own party– say they wouldn’t consider supporting him for president were he the GOP nominee.

See PDF with full results, charts and tables.

How long the Trump surge lasts is an open question; this poll was conducted Thursday through Sunday, mostly before his controversial criticism Saturday of Sen. John McCain’s status as a war hero. And Trump’s support was conspicuously lower Sunday than in the three previous days.

Trump’s frontrunner status, moreover, reflects the crowded GOP race. He leads the 16-candidate field with 24 percent support among Republicans and Republican-leaning independents who are registered to vote, up sharply from 4 percent in May. While enough for a lead, that also means 76 percent prefer someone else, or none of them.

Scott Walker has 13 percent support, Jeb Bush 12 percent, with the rest in single digits.

Trump’s support was 28 percent in this survey’s first three nights of polling. While the sample size of registered leaned Republicans on Sunday is quite small, he dropped to the single digits that day.

His improvement overall, compared with an ABC/Post poll in May, occurred largely across the board. Support for Rand Paul dropped by 5 percentage points, for Ted Cruz by 4 and for several other candidates by generally non-significant 1- to 3-point margins.

Among groups, Trump’s advanced since May by 7 points among college graduates, but just to 8 percent, underscoring his weakness in this group. But – at least until Sunday – his gains otherwise were broad, up, for example, by 16 points among Republicans, 23 points among GOP-leaning independents and 20 points among moderates and conservatives alike.

He’s at least numerically ahead, as a result, across many key groups.

Nativists

There’s a nativist element to Trump’s support: He’s backed by 38 percent of Republicans and GOP-leaning independents who feel that immigrants, overall, mainly weaken U.S. society. That drops to 12 percent among those who say immigrants strengthen this country.

Another, related result underscores a disconnect for Trump with the public overall, one that may pose a challenge for him in the future. Seventy-four percent of Americans see undocumented immigrants from Mexico as “mainly honest people trying to get ahead” as opposed to “mainly undesirable people like criminals.” Trump, again controversially, has said such immigrants include drug dealers and rapists, while “some, I assume, are good people.”

The question of core values is a potentially difficult one for Trump. Republicans and Republican-leaning independents by a 24-point margin, 56-32 percent, say his views do not reflect the core values of the Republican Party (leaned Democrats agree, by a similar 61-32 percent). And 31 percent of Republicans say they wouldn’t consider voting for Trump were he the party’s nominee – a large group to lose on his own side. (Just 11 percent of Democrats, by contrast, rule out supporting Hillary Clinton.)

General

In a general election trial heat, Clinton leads Bush, the GOP fundraising leader, by a slight 50-44 percent among registered voters. But with Trump as an independent candidate that goes to 46-30-20 percent, Clinton-Bush-Trump – with Trump drawing support disproportionately from Bush, turning a 6-point Clinton advantage into 16 points.

Trump’s support in this three-way matchup was 21 percent from Thursday to Saturday, vs. 13 percent in Sunday interviews.

These are early days, of course; leaders came and went like flashcards in the 2012 Republican primary contest, and, as noted, potential fallout from Trump’s comments on McCain – or his next pronouncements – remains to be seen. But the results underscore the GOP’s conundrum in responding to Trump, a billionaire businessman and television celebrity who hasn’t ruled out an independent run for the presidency.

Among other results in this poll, produced for ABC by Langer Research Associates:

The Dems

Clinton retains very broad backing for the Democratic nomination, 63 percent, vs. 14 percent for Bernie Sanders and 12 percent for Joe Biden. With Biden out (he hasn’t announced a candidacy), most of his support goes to Clinton, boosting her to 68 percent.

That said, Clinton’s support is less enthusiastic than it might be – 42 percent of her supporters are very enthusiastic about her candidacy. And while 72 percent of leaned Democrats are satisfied with their choice of candidates, that compares with 83 percent at this point in 2007.

Sixty-nine percent of Democrats and Democratic leaning independents call Clinton “about right” ideologically, as opposed to too liberal or too conservative. That falls to 40 percent for Sanders – not because he’s seen as too liberal, but because nearly four in 10 don’t know enough about him to say. Also, despite Sanders’ more liberal image, Clinton wins 64 percent support from liberals.

She also does 19 points better among women than men in support for the nomination, and 15 points better among nonwhites than whites.

More GOP

Republican candidates do less well in their base than Clinton in hers on being seen as “about right” ideologically – 46 percent for Bush, 45 percent for Marco Rubio, 44 percent for Trump, 38 percent for Walker and 35 percent for Ted Cruz.

Twenty-two percent call Bush “too liberal” and 17 percent say the same about Trump. Walker, Cruz and Rubio, like Sanders, have high undecided numbers on the question.

As shown in the table above (online readers, see the pdf), Bush is notably weak among very conservative leaned Republicans, with just 6 percent support – a persistent difficulty for him.

General

A general election match-up between Clinton and Bush is a bit better for her now (50-44 percent, as noted) than in May, 47-44 percent. That relies, in part, on a 19-point advantage for Clinton among moderates. (She has 21 percent support among conservatives; Barack Obama won 17 percent of that group in 2012). Clinton also does 10 points better among women than men (as did Obama) and far better among under-30s (71 percent support) than their elders, especially seniors (40 percent). And she has 78 percent support among nonwhites vs. Bush, compared with 39 percent of whites – margins again similar to Obama’s in 2012.

Bringing Trump into the mix as an independent reduces Bush’s support in his better groups, including Republicans (-27 points for Bush with Trump added), conservatives (-23) and whites (-19).

Another result marks the mood confronting both political parties: Asked which better represents their own values, a substantial 23 percent of Americans volunteer that neither does (of the rest, 38 percent pick the Democrats, 31 percent the Republicans). And in a challenging finding for candidates trying to find a lever, the public fractures on what attributes matter most to them – a strong leader (24 percent, peaking among Republicans), one who’s honest and trustworthy (also 24 percent), one who shares their values (20 percent) or who understands their problems (17 percent, peaking among Democrats). Two other items finish lower on the list – having the best experience (10 percent) or the best chance to win (3 percent).

And the pres

As to the president (not the chief focus of this survey, clearly), Obama continues to encounter difficulties in his popularity overall. While 45 percent of Americans approve of his job performance, more, 50 percent, disapprove, essentially unchanged from 45-49 percent in May. Despite recent economic gains he manages just an even split on handling the economy, also unchanged. Views of the president remain highly polarized.

Methodology

This ABC News/Washington Post poll was conducted by landline and cellular telephone July 16-19, 2015, in English and Spanish, among a random national sample of 1,002 adults, including 815 registered voters. Results have a margin of sampling error of 3.5 points for the full sample, and 4.0 for registered voters, including design effect. Partisan divisions are 30-21-39 percent, Democrats-Republicans-independents.

Interviews were conducted Sunday among 200 respondents overall, including 82 Republicans and Republican-leaning independents and 65 leaned Republicans who reported being registered to vote. ABC customarily reports results for groups at or near 100 respondents, but may make characterizations of results in smaller groups. Sunday results on Trump support characterized in this analysis were essentially identical regardless of registration.

The survey was produced for ABC News by Langer Research Associates of New York, N.Y., with sampling, data collection and tabulation by Abt-SRBI of New York, N.Y.