By Patricia Zengerle

CHARLOTTE, North Carolina (Reuters) - At their national convention last week in Tampa, Republicans tried to improve their sagging numbers with minority voters by touting a racially diverse list of speakers - a contrast to the largely white crowd of delegates there.

This week in Charlotte, Democrats are putting on their own show of diversity, with Hispanics, Asian- and African-Americans not only on the podium, but also throughout the sections of delegates.

But Democrats in Charlotte here acknowledge a rising concern about a growing electoral problem: the party's flagging popularity with white men.

Polls show Democratic President Barack Obama - the first black U.S. president - trailing Republican Mitt Romney by 20 points among white men two months before the November 6 election.

The gap, which has largely negated Obama's advantage among minorities, is significant enough that Democrats are looking to minimize the damage to Obama and other party candidates, rather than win the "white guy" vote.

Polls give Obama strong leads among minority voters in a year when the Republican nominee has been accused of trying to beef up his support among white voters by running advertisements with subtle racial appeals.

To win in November, Democrats still need a strategy for carving into Romney's advantage among white men.

One plan is this: Try to appeal to older white men by emphasizing Democrats' efforts to protect Medicare, the government's popular health insurance program for Americans aged 65 and over, against Republicans' plans to impose changes that Democrats say could dramatically reduce its benefits.

Democrats have seized Romney's choice of Wisconsin Congressman Paul Ryan as his running mate to attack the Republican ticket over Medicare. Ryan proposed a plan two years ago to transform Medicare into a program in which recipients would use vouchers to pay for private insurance.

He later modified the plan to let users keep traditional Medicare, but they would still use vouchers to pay for it.

ATTACKS AND COUNTER-ATTACKS

Democrats attack the "Romney-Ryan" plan as a bid to "destroy" Medicare and turn it into a "coupon" program.

Republicans counter that Obama cut $716 billion from Medicare to pay for his healthcare overhaul - even though Ryan proposed similar cuts in his own budget plan.

"Medicare is a huge issue, which is why Democrats are talking about it," Democratic strategist Bud Jackson said. "Medicare is a popular program, so when you propose to change it, obviously, it's going to raise a red flag."

Former President Bill Clinton, a favorite Democratic ambassador to working-class whites, devoted several minutes to Medicare during his convention speech nominating Obama for re-election on Wednesday night, saying Obama and the Democrats strengthened the program, and Republicans would destroy it.

There are signs that the strategy could work for Democrats. A Pew poll released on August 21 found that 49 percent of Americans oppose the Medicare voucher plan, compared with just 34 percent who support it.

"The older independent white males that we might think of as being traditionally Republican ... are obviously those that are eligible for Medicare," said Ange-Marie Hancock, a political scientist who studies race issues at the University of Southern California.

If Democrats can persuade such voters that Republicans' plans would damage Medicare, "then they can kind of mute the issue that Democrats are seen as the party of minorities," she said.

AN EPISODE IN TAMPA

The issue of race looms large in the electoral calculus that will decide the presidential race - and in the makeup of the political conventions that Americans have seen during the last two weeks.

Twenty-seven percent of the Democratic delegates in Charlotte are black, compared with about 2 percent of the Republican delegates in Tampa.

In Tampa, it was clear from Republicans' choice of speakers - including former secretary of state Condoleezza Rice, the first black woman secretary of state, and Florida Senator Marco Rubio, a Cuban American - that party leaders had made a point of trying to attract minorities.

But the efforts were undermined somewhat when two alternate delegates to the convention were ejected for throwing peanuts at a black camerawoman for CNN, whom they had called an animal.

The episode in Tampa came at a time when Democrats were accusing Republicans of subtly trying to appeal to whites by running ads that falsely claimed Obama was ending work requirement for welfare recipients.

Democrats seized on the ad as a "dog whistle" that was intended as a signal to judge black Americans as "welfare queens."

"It has really gotten into folks' heads that welfare and blackness are tied together," said Andra Gillespie, a political scientist at Emory University in Atlanta, noting that more white Americans than blacks use the government assistance program. "For him (Romney) to talk about welfare is for him to bring up race without actually bringing up race."

Romney's chief advertising strategist, Ashley O'Connor, has rejected such analyses of the Republican campaign's goals, and told the National Journal last week that the welfare ad had been among the Romney campaign's most effective television spots.

The attacks were on the minds of Democrats in Charlotte for the convention that formally nominated Obama for re-election on Wednesday.

"I think the Republican Party uses a lot of code words, like welfare and food stamps," said Seeta Begui, a nurse and radio host who is a Democratic delegate from Florida. "They scare the electorate into thinking we're going to take your money and give it away."

(Editing by David Lindsey and Alden Bentley)