A new national Quinnipiac University poll finds Donald Trump leading the crowded Republican presidential primary field with 20 percent support, even as 30 percent of registered Republican voters say there is "no way" they would support him for president. The New York reality TV star and real-estate magnate is trailed by Wisconsin governor Scott Walker, at 13 percent support, and former Florida governor Jeb Bush, at 10 percent.

Ben Carson, Mike Huckabee, Rand Paul, and Marco Rubio all have six percent support while Ted Cruz and John Kasich have 5 percent and Chris Christie has 3 percent.

This is a big jump for Trump in the Quinnipiac poll; in May, he registered just 5 percent support. Dropping the most support since May are Carson, Huckabee, and Rubio, who each registered 10 percent support two months ago.

Although he leads the GOP field in this latest poll, Trump doesn't poll so well against his potential Democratic opponents in the general election. Hillary Clinton, who holds a commanding lead of 55 percent among registered Democratic voters, is currently beating Trump 48 percent to 36 percent. Vice President Joe Biden, who is not yet in the race, earns 49 percent support to Trump's 37 percent, and Vermont senator Bernie Sanders has 45 percent to Trump's 37 percent.

The other top Republicans are a little more even with Clinton. Bush has a one-point edge on her, 42 percent to 41 percent, while Clinton leads Walker by a single point, 44 percent to 43 percent.