Presidential conventions are designed to patch up partisan disagreements — or at least to project a compelling pitch of the party's core message as voters tune in to the general election campaign. But a new Washington Post-ABC News poll finds a significant share of Democrats and Republicans disagree with their party on potential wedge issues and are not committed to supporting the party's nominee. Yet.

The poll asked what position Americans want the next president to take on immigration, abortion, gun laws and trade agreements, and found a greater share of the public endorsing Democrats' position on three issues. Sixty-percent of adults want the next president to support a path to legal status for undocumented immigrants, 52 percent want a president who supports legal abortion in most cases, and 57 percent want a president who supports stricter gun laws, all roughly in line with recent polling.

Three-quarters want a president who supports free trade agreements; the Democratic Party platform is more positive about free trade agreements than the Republican Party, which endorses agreements negotiated by President Ronald Reagan but also blames China and others for stealing American technology. Yet Hillary Clinton has also come out in opposition to the Trans-Pacific Partnership, the most recent major agreement under consideration, indicating neither party is fully for or against trade agreements.

Most Republicans and Democrats agree with their party's broad position on immigration, guns and abortion, but a sizable minority do not. One in three Republicans and Republican-leaning independent voters say the next president should support a path to citizenship for undocumented immigrants and support legal abortion, while almost as many (28 percent) support stricter gun control laws.

While Democratic-leaning registered voters are more unified, there's still some discord, with 1 in 6 opposing a path to citizenship and roughly 1 in 5 opposing legal abortion and stricter gun control laws.

Disagreeing with one's party on a single issue is one thing, but that ideological discord may not matter if the issue is unimportant. To account for this, the Post-ABC poll also asked how important it was that the next president hold each policy position, and combined results to identify a set of "persuadable voters" who (1) disagree with their party on immigration, abortion or gun control and (2) say it's extremely or very important that the next president adopt their approach.

By this definition, 33 percent of Republicans are persuadable voters on these three issues while 23 percent of Democrats are persuadable. Such cross-pressured voters have the potential to be lured to support candidates of the other major party, according to research by political scientists Sunshine Hillygus and Todd Shields.

Crossover potential was clear in The Post-ABC poll. While 90 percent of Democrats who are not persuadable support Democratic presumptive nominee Hillary Clinton against Donald Trump, that drops to 67 percent among persuadable Democrats. Likewise, Trump garners 89 percent support among issue-aligned Republicans, but only 65 percent among persuadable Republicans.

Among all registered voters, Trump nets about 2 percent support among Democratic-leaning voters that disagree with their party on an issue they say is important. By contrast, Clinton nets 3 percent among Republicans who disagree with their party on an important issue. The number of actually persuadable voters would be larger, of course, if more than three issues were taken into account.

Parties have some useful tools to help bring these voters back into the fold — most of all, their dislike of the other party. Roughly three-quarters of persuadable Republicans dislike Trump and a similar share of persuadable Democrats dislike Clinton. As The Post's Dan Balz noted, Republican convention speakers more often emphasized Clinton's flaws than Trump's virtues during the first speeches.

Whatever internal party disagreements, Democrats and Republicans overwhelmingly unite behind their party's presidential candidates by November, and over 90 percent did so in 2012. But that level of unity comes after months of high-volume campaigning by both major parties. So far Clinton and Trump have not achieved that level of party support, and the coming weeks will  show how much the conventions helped bring fellow partisans together.

The Post-ABC poll was conducted July 11-14 among a random national sample of 1,003 adults reached on cellular and landline phones. The margin of sampling error for overall results is plus or minus 3.5 percentage points. Full methodological details are available here.

Emily Guskin contributed to this report.