Washington (CNN) Across three domestic issues that are shaping up to be more important to the 2016 presidential election than they were in 2012 -- gun control, illegal immigration and abortion -- polling generally suggests Democrats have the upper hand in terms of public opinion, but a new CNN/ORC Poll finds the nuances in views on these issues don't always favor one party over the other.

All three have become increasingly important to voters and prominent within the campaign itself and could come up during Wednesday's Republican debate hosted by CNN in Simi Valley, California.

In June 2011, 22% of voters called gun policy an "extremely important" issue in their vote for president, that's risen 20 points since to 42%. Likewise, 29% called illegal immigration a top issue in June 2011, that's up 10 points to 39%, while the share calling abortion an extremely important issue is up 7 points to 27%. Here's a look at where the public stands on each.

Gun policy

Most polling has shown the public broadly in favor of expanded background checks for gun buyers and preventing those with mental health issues from purchasing guns, but the new poll shows majorities think current laws are about right or even too harsh, and doubt that expanded background checks would keep guns out of the hands of the mentally ill or convicted criminals.

Overall, 41% say existing laws make it too easy for people to buy guns, down from 56% saying so about a month after the shooting deaths of 27 people at an elementary school in Newtown, Connecticut. About half, 49%, say current laws are about right, and 10% that they make it too difficult to buy a gun.

These mixed overall views mask sharp divides by sex, partisanship, age and urbanity. Among women, 52% say the current laws make it too easy to buy a gun, while just 30% of men agree. Two-thirds of Republicans, 65%, think current laws are about right, just 28% of Democrats agree. And a majority of seniors, 51%, say it's too easy to get a gun, while only 37% of those under age 50 think the same. Urban residents are more apt than suburbanites or rural residents to say it's too easy to get a gun, 46% who live in urban areas say that compared with 40% in the suburbs and 37% in rural areas.

At the same time, many express doubts that expanded gun laws would be able to prevent those with mental health problems from buying guns (44% see that as likely, 56% unlikely), or that such laws would keep guns out of the hands of convicted criminals (42% say that's likely, 58% unlikely). But most also say it wouldn't necessarily make it harder for a law-abiding citizen without mental health problems to buy one, 57% say it's unlikely to do that.

Even among those who say it is now too easy to buy a gun, just small majorities believe that implementing more comprehensive background checks for all gun purchases would be likely to stop gun purchases by the mentally ill (53%) or convicted criminals (55%).

President Barack Obama receives mostly negative reviews for his handling of gun policy, 59% disapprove of his handling of the issue on which he said he's been the "most frustrated and most stymied" during his presidency; just 35% approve of his work. That's worsened since a June poll, and nears his 2014 low of 33% approval on it. That drop off comes particularly among liberals. In the new poll, just 53% of liberals approve of Obama's handling of gun policy, down from 63% in June. Among moderates (44% then, 41% now) and conservatives (23% then, 19% now), the declines have been smaller.

Immigration

Illegal immigration has become a defining issue in the race for the Republican nomination for president, as GOP front-runner Donald Trump has focused his campaign on claims that illegal immigration is destroying the country and his ideas for solving the problem. Most Americans say the solutions ought to focus more on border security and a path to citizenship over deportation, but about half are receptive to Trump's proposals including building a wall along the entire border with Mexico and ending birthright citizenship for children of those in the country illegally.

Asked whether the nation's top priority in dealing with illegal immigration should be deporting those already in the country, developing a plan to stop new illegal immigration, or developing a plan to allow those already in the U.S. illegally with jobs to become legal residents, a plurality say a plan to make those here illegally legal residents is most important (46%), next, 39% chose border security, and just 14% called deportation the top priority.

Border security leaps to the top of the list when Americans are asked what the next priority should be, with 88% overall choosing it as a first or second priority, 70% choosing a path to legal residency and 37% deportation. Republicans are most apt to have selected deportation as a top or second priority, 48% do so, compared with 38% of independents and 26% of Democrats.

Still, 52% say they favor building a fence along the entire border with Mexico, up from 45% who backed that idea in 2006. The public is more evenly divided on ending birthright citizenship for children born to parents in the country illegally, 50% say such children should be granted automatic citizenship, 49% that they should not.

Among Trump's backers, 87% support building a fence between the U.S. and Mexico, and 82% think children born to parents in the U.S. illegally should not be granted citizenship. Republicans who do not support Trump tend to agree with these views, but there's greater dissent than among Trump's backers: 65% support a fence between the U.S. and Mexico, 67% ending birthright citizenship.

Despite Trump's claims that Mexico has been intentionally sending their least desirable citizens to the U.S. illegally and poses a threat to the nation, just 37% say they see Mexico as a threat to the United States, that's well below the share that see Iran (82%), North Korea (76%) or Russia (70%) as a threat to the nation.

Among Republicans, however, 56% say they think Mexico is a threat, just 23% of Democrats and 37% of independents agree. Trump supporters are particularly apt to see Mexico as a threat, 64% say so compared with 48% of Republicans who do not back Trump.

Trump may be having more of an impact when it comes to perceptions of China's threat to the U.S. About 73% in the new poll said they see China as a serious threat, up from 54% in April, with the share calling China a "very serious threat" nearly doubling from 18% to 33%.

Abortion

A congressional fight looms over funding for Planned Parenthood following the release this summer of several secretly recorded, heavily edited videos of Planned Parenthood employees discussing the sale of fetal tissue for scientific research, but the new CNN/ORC Poll shows the public would much rather continue funding Planned Parenthood than face a government shutdown.

About 71% say it's more important for Congress to approve a budget agreement that would avoid a government shutdown than to defund Planned Parenthood, 22% say it's a bigger priority to eliminate the organization's federal funding. That's more saying it's important to avert a shutdown now than in September 2013, just before a budget fight over federal funding for some portions of the Affordable Care Act led to a partial government shutdown.

In the new poll, 87% of Democrats and 74% of independents say avoiding a shutdown is the key priority, while Republicans are just about evenly divided, with 48% saying avoiding a shutdown is more important and 44% saying ending Planned Parenthood's funding is most important.

Even among those who say abortion should be illegal in all or most cases, however, 63% say it's a higher priority for the government to approve a budget and avoid a shutdown than to eliminate funding for Planned Parenthood.

A CNN/ORC Poll conducted in August found that most Americans (66%) said that in general, the federal government should continue to provide funding for Planned Parenthood, 31% that the organization's federal funding should be eliminated. That's about the same as in April 2011, when some Republicans in Congress tried to cut funding for Planned Parenthood from the federal budget.

Overall, 39% of adults in the new poll think abortion should be legal in most circumstances, 58% that it should be illegal in most.

The CNN/ORC Poll was conducted by telephone Sept. 4-8 among a random national sample of 1,012 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points.