WASHINGTON, March 4: Voters turned out in large numbers in Texas and Ohio on Tuesday for Democratic primaries that may make Barack Obama the first ever non-White presidential nominee for a major US party.

Former first lady Hillary Clinton needs convincing victories in both the states to win the Democratic Party’s nomination for the 2008 presidential election.

Primaries in the two smaller states of Vermont and Rhode Island – also on Tuesday – may prove crucial in such a tight race.

Both candidates said they were confident to win, but their campaign teams conceded that the contest was too close to call. “I feel really good about today,” Mrs Clinton told reporters after a visit to a polling station in Houston, Texas. “I think it’s going to turn out well.”

Mr Obama was equally confident. “We know this has been an extraordinary election,” he said. “We’re working hard to do as well as we can.”

Both candidates need to get as many of 370 delegates up for grabs on Tuesday as possible. Of the four primary contests, the one in Texas is the most coveted as it offers the largest number of delegates, 193, followed by Ohio, 141, Rhode Island, 21, and Vermont,15.

If super-delegates, party officials who are not elected but have the right to elect the presidential nominee, are also included, then a combined total of 389 delegates are at stake in Texas and Ohio.

Mr Obama is leading Mrs Clinton by 1,383 delegates to 1,276. The Democratic candidate needs 2,025 delegates to win the nomination. Latest opinion polls show Mrs Clinton and Mr Obama running neck and neck in Ohio and Texas.

In Texas, Mr Obama leads Mrs Clinton by 47 per cent to 44 per cent.

In Ohio, according to the Reuters/C-SPAN/Houston Chronicle poll, Mr Obama garners 47 per cent to Clinton’s 45 per cent. Other polls also show Mrs Clinton and Mr Obama in a tight race.

An MSNBC/McClatchy/Mason-Dixon survey has Mr Obama leading by one point in Texas, 46 per cent to 45 per cent. A Cleveland Plain Dealer/Mason-Dixon poll, meanwhile, has Mr Clinton ahead in Ohio, 47 per cent to 43 per cent.