As the behind-the-scenes battle for delegates between Donald Trump and Ted Cruz intensifies and devolves into nastiness, Democrats are laying the groundwork to capitalise on the scenes of chaos that seem likely to erupt at a contested GOP convention and in its aftermath, in hopes of giving Hillary Clinton a boost even before the general election gets under way.

In a preview of what’s to come along these lines, the pro-Clinton Super PAC Priorities USA has just rolled out a new web advertisement: “GOP Split Widens to a Chasm”.

It is reasonable to assume that, if a contested convention does happen, you will see a lot more along these lines, including paid adverts designed to contrast continuing Republican craziness with what many senior Democrats see as one of Clinton’s strong suits — that, for all her very real personal negatives, Americans believe she has the right kind of temperament to be president.

“The mess they find themselves in will continue to be a telling contrast between the two parties as they head to the general election,” Priorities USA spokesman Justin Barasky says.

“While Hillary Clinton and the Democrats talk to the American people about how to raise wages, break barriers and keep our country safe, Republicans will descend into chaos and nastiness that will hobble their eventual nominee.”

A new national poll further underscores the sort of chaos that could attend a contested convention.

Yesterday’s NBC News/Survey Monkey Tracking poll finds: “Only about half of Cruz supporters and half of Trump supporters said they would vote for the other GOP candidate in a general election should the Democratic candidate be Hillary Clinton.”

While this may overstate the case, what this means is that the possibility of a split party remains very real, whether the nominee is Trump or Cruz. This polling suggests that if Trump wins the nomination — say, on the first balloting at a contested convention — a non-trivial number of Republicans could defect in the general election.

But this polling also suggests that something similar may also happen if Cruz wins the nomination.

If Trump wins the most delegates via the voting but falls short of a majority, and the nomination goes to Cruz at a contested convention, Trump may do all he can to wreak havoc by calling on his supporters to sit the election out — and it may, to some degree, work. Trump has already vowed, er, predicted that “riots” could take place.

Indeed, Byron York writes in the Washington Examiner that such an outcome could present the GOP with its own Bush vs Gore moment, in which the nomination was given to “the candidate who lost the popular vote”, leaving behind “diminished faith in the legitimacy of the electoral system” among Republicans. Trump will likely exploit this to cast the whole process as illegitimate and symptomatic of the same elite corruption and disdain for regular voters that he has been railing at for months.

And so, convention craziness could conceivably hurt the GOP in two ways. First, it could create impressions of a party in chaos even as Clinton, should she win the nomination, begins laying out her general election agenda.

Second, even if that blows over, intra-GOP bitterness and recriminations could continue to divide the Republicans after the convention has come and gone.

Of course, any Democrat hopes of capitalising on GOP contested-convention chaos also underscore the importance of a relatively orderly resolution to the Democratic primary battle.

Given the intimations that we have been hearing from the Sanders camp about a contested Democratic convention, such an outcome is anything but assured.

But it looks substantially more likely than an orderly resolution on the GOP side.

•Greg Sargent writes The Plum Line blog for The Washington Post