PPP’s new Presidential poll in Iowa finds a tight race in the general election for President in the state. Hillary Clinton leads 7 of her Republican opponents while trailing 4 of them, but in none of the cases are the margins larger than 4 points.

The strongest Republican against Clinton in the state is Ben Carson, who leads her 44/40. The other three GOP hopefuls ahead of Clinton all lead her by just a single point- Mike Huckabee at 44/43, Scott Walker at 44/43, and Marco Rubio at 43/42.

The Republicans who fare the worst against Clinton are Jeb Bush who trails by 4 at 44/40, and Rand Paul and Donald Trump who each trail by 3 at 43/40. The rest of the GOP hopefuls each trail Clinton by 2 points- Ted Cruz at 44/42, Carly Fiorina at 42/40, and Chris Christie and John Kasich each at 41/39.

When we last polled Iowa in April Clinton led the 8 Republican hopefuls we tested on this poll by an average of a little bit more than 4 points. Now her lead over those same eight comes out to an average of half a point. Bernie Sanders is also catching up to Clinton when it comes to match ups with the Republicans as he becomes better known- he leads Bush 41/40, trails Rubio 39/38, leads Trump 44/40, and ties with Walker at 40. On the whole he does only fractionally worse than Clinton in the head to heads.

The specter of a Donald Trump independent candidacy continues to be a serious threat to the GOP. In a three way contest he would get 21%, with Clinton’s lead over Bush rising to 9 points at 39/30. Trump gets 29% of the Republican vote and 28% of the independent vote as a third party candidate, while only taking 8% of Democrats. Trump’s 21% standing as an independent becomes a little less impressive when you consider that Deez Nuts also polls at 7% as an independent, which sort of suggests that might be the floor for a third party candidate. (Clinton leads Trump 41/36 in the iteration of the horse race including Mr. Nuts.)

Chuck Grassley looks to be in pretty good shape for reelection next year. He has a 52/32 approval rating, easily making him the state’s most popular politician and making him one of the more popular Senators in the country on top of that. He leads his prospective Democratic opponents by anywhere from 22 to 24 points- it’s 51/29 over Bob Krause, 53/30 over Tom Fiegen, and 52/28 over Rob Hogg. The Democratic candidates are all little known, with name recognition ranging from 18% to 22%, so there could be some tightening down the road but Grassley is in a pretty good place to start.

Terry Branstad is not terribly popular right now, with 42% of voters approving of him to 47% who disapprove. Voters in the state are pretty unhappy with several of Branstad’s recent actions. Only 34% approve of his recent veto of funding for the major universities in the state, compared to 49% opposed to that action. There’s even less support for his recent veto of funding for K12 education in the state- that meets with 29% support and 57% opposition. But the most unpopular recent action of all is his veto of the bipartisan plan to keep open 2 of Iowa’s 4 mental health institutions. Just 20% of voters support him on that issue to 63% who are opposed, and on that one even Republicans are opposed to his action with only 37% in favor of and 42% against it.

Finally we polled a trio of major national issues. 72% of voters in Iowa support increasing the minimum wage to at least $10 an hour, with only 23% in support of keeping it at $7.25 or eliminating the federal minimum wage all together. Even among Republicans there’s 54% support for at least going to $10.

There’s 85/8 support for requiring background checks on all gun purchases, and strong support for that holds true across party lines- 94% of Democrats, 82% of independents, and 78% of Republicans support it.

And Iowans continue to think that gay marriage being legal is no big deal- 76% of voters, including 62% of Republicans, say its being legal has either had a positive impact on their lives or none at all. Just 24% claim it’s been a negative thing.

Full results here