In a possible sign that President Obama's political coattails aren't long enough to help Democrat Hillary Clinton, a new Democratic poll shows that she would lose the key battleground state of Ohio big, potentially crushing her White House bid.

The poll showed that Clinton would lose 47 percent to 40 percent to Ohio Gov. John Kasich, who is likely to enter the race. But that's not all. She would also lose to Kentucky Sen. Rand Paul, 44 percent to 41 percent, and tie Sen. Marco Rubio at 44 percent.

"The key to Kasich's advantage is that 89 percent of Republicans support him, compared to 75 percent of Democrats for Clinton," said the latest survey from Public Policy Polling of the former House member and budget expert.

Ohio Gov. John Kasich is popular in his state and considering a presidential bid. AP Photo

"Kasich is pretty universally popular with Republican voters in the state, 72 percent approve of the job he's doing to only 17 percent who disapprove," said the PPP analysis.

Paul's campaign noted that it was the latest good news poll for the candidate. "This poll, like others, shows that Sen. Rand Paul is the best Republican to beat Hillary Clinton in 2016. Ohio is one of the most important swing states in the pathway to the White House, and no Republican has won it since 2004. In the primary, Sen. Paul is tied for first nationally and in New Hampshire and he is tied for second in Iowa. In the general election, he is leading the field against Hillary Clinton and ahead of her in Ohio and other key states including Arizona, Iowa, New Hampshire, and Pennsylvania," said spokesman Sergio Gor.

Kasich made news today by hiring two top officials who would run his campaign.

But they also like Rubio, said PPP. "Rubio has the highest favorability rating among GOP voters in Ohio, as we have found to be the case many places lately, at 58/16," said the poll.

Not so for New Jersey Gov. Chris Christie, though. "Ohio makes yet another state where Christie is outwardly disliked by GOP voters. His favorability is 34/44. To put into perspective how poor that is the next least popular Republican we tested — Jeb Bush — is still at +16 at 48/32," said PPP.

The importance of Ohio can't be overstated. It was one of the keys to both of Obama's elections.

Paul Bedard, the Washington Examiner's "Washington Secrets" columnist, can be contacted at pbedard@washingtonexaminer.com.