By Steve Holland and Deborah Charles

WASHINGTON (Reuters) - For Democratic President Barack Obama, Republican-leaning Indiana suddenly might be a little more winnable in the November 6 election.

But North Carolina, a politically divided state where Obama will be in a close battle with Republican Mitt Romney, may have just gotten a little tougher for the president.

Those were among the themes to emerge from uprisings among conservative voters in each state on Tuesday. Indiana Republicans ousted their longtime senator, Richard Lugar, and North Carolina voters approved a ban on same-sex marriage, highlighting a politically touchy subject on which Obama clarified his views on Wednesday by saying for the first time he supported such unions.

In pushing aside Lugar, the longest-serving Republican in the U.S. Senate at 35 years, Indiana Republicans placed their bets on conservative Tea Party candidate Richard Mourdock in the November race against Democrat Joe Donnelly.

The result will almost certainly make Indiana's Senate race one of the marquee contests in November - and is potentially good news for Obama.

Without Lugar on the ballot, Democrats are certain to give more attention - and money - to Donnelly's cause while trying to prevent Mourdock from adding to the growing ranks of compromise-resistant conservatives in the Senate, which Democrats are seeking to hold in the November election.

Analysts said more ads by Democrats, along with Lugar's absence from the ballot, could help Obama in Indiana, which he won over Republican John McCain in the 2008 election but where he has trailed Romney, the presumptive Republican nominee, in recent polls.

TROUBLE FOR OBAMA?

In the swing state of North Carolina, the rejection of gay marriages put a focus on Obama's challenge in putting together the type of voting coalition he used in defeating McCain there four years ago.

Before Wednesday, Obama tried to walk a fine line on the question of same-sex marriage, saying gay and lesbian couples should have the same rights as married straight couples, although he opposed same-sex marriages.

But on Wednesday, three days after Vice President Joe Biden said on NBC's "Meet the Press" that he supported legalizing same-sex marriages, Obama said in an interview with ABC that he too believed they should be legal.

Obama won North Carolina in 2008 with a huge turnout in urban areas and among black voters. He also did well among white suburban voters, in part because many of them liked his economic pitch more than they disliked his support for gay rights, according to exit polling.

Tuesday's vote revealed a motivated conservative electorate in North Carolina, one of 10 politically divided states likely to decide the presidential election, and raised questions about whether Obama can count on the same formula this November.

"It's bad for Obama," said Merle Black, a political science professor at Emory University in Atlanta. "It shows a huge vulnerability on this kind of an issue."

Tuesday's vote led some pro-gay rights groups to circulate petitions urging Democrats to move their national convention from Charlotte.

Democratic officials dismissed that notion and said the convention - where Obama will formally be nominated for a second term - would go on as scheduled in Charlotte in early September.

WEST VIRGINIA WEIGHS IN

Obama is unlikely to win the conservative state of West Virginia in the November election. The Democratic primary there on Tuesday offered a hint why.

In the primary, Keith Judd, a pony-tailed prisoner serving a 17 1/2-year sentence in Texas for extortion, won 43 percent of the vote, to Obama's 57 percent.

Romney, asked by Denver's KOA radio about a split in the Republican Party, said the West Virginia vote was evidence of a rupture in the Democratic Party.

"If there's a rift in the party, I think it's his," Romney said of Obama. "I saw in West Virginia, for instance, an inmate got almost 40 percent of the vote against President Obama. ... So I think they've got more problems on that side of the aisle than we do on ours."

(Editing by David Lindsey and Peter Cooney)