WASHINGTON (CNN) -- Sen. John McCain is aiming to persuade Sen. Hillary Clinton supporters to forget about party unity and side with him instead during a campaign stop in the swing state of Ohio.

At first glance at a General Motors auto plant in Lordstown, Ohio, on Friday, McCain's push for fuel-efficient cars was not just about the cars, it was about the workers -- blue-collar voters.

They are the kind of voters who Clinton won in the Democratic primary and who McCain wants badly.

"The brunt of this incredible increase in oil is being borne by the lowest-income Americans. And that's not fair," McCain said.

In fact, Clinton came to the same plant before she beat Obama in Ohio, with the same message McCain is using against him now: empty words.

"Speeches don't fill up your tank or fill your prescription or do anything about that stack of bills that keeps you up at night," Clinton said in February.

On Friday, McCain told the audience that he thinks "we are able to attract some of Sen. Clinton's supporters, not so much because of any reason that they think that I may serve America best."

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McCain advisers say that if they have any chance at winning battleground states like Ohio and Pennsylvania, they need to lure Clinton supporters. Interactive: CNN's Electoral Map »

A Quinnipiac University Poll released June 18 shows that they are.

A large percentage of Clinton's Democratic primary voters in Ohio -- 25 percent -- say they'll vote for McCain. It's roughly the same in Pennsylvania. Read more on the Quinnipiac Poll

But for McCain, that's not enough. He is trailing in both pivotal states.

Still, McCain needs to hold onto Clinton supporters leaning his way. It's not easy when she's telling them to vote Obama.

"We may have started on separate paths. ... Today, our hearts are set on the same destination for America ... to elect Barack Obama as the next president of the United States," Clinton said. "We are one party; we are one America."

So when a woman in a Hillary hat told McCain at the rally that there are lots of women who feel disenfranchised, McCain responded:

"May I say that all of us respect Sen. Clinton and the race that she ran. She inspired millions of Americans and millions of American women and women all over the world."

CNN political producer Ed Hornick contributed to this report.

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