Kentucky and Oregon will hold primaries on that day, and he said the results may vault him over the top in terms of numbers of elected delegates.

In that case, he said in a TV interview on Thursday using baseball language: 'We can make a pretty strong claim that we have got the most runs and it's the ninth inning and we have won.'

The Obama campaign says he needs just 33 more pledged delegates to clinch a majority of the Democratic nominating officials, 1,606.

This calculation leaves out the superdelegates - party officials not bound to vote as their states did - whose support will eventually determine who the winner is.

Still, it will be a milestone.

As the race appeared to be winding up, Mr Obama was received like the winner in the Capitol when he made a surprise visit to the floor of the House of Representatives on Thursday.

He was mobbed by Congressmen, some of them known Clinton supporters, and some Republicans as well. He spent 45 minutes shaking hands on the floor of the House.

The media here quickly dubbed it his 'victory lap'.

Over at the Clinton camp, her top aide has said she is not likely to hang on after June 3 - the day of the last primary contest.

Addressing concerns over a summer-long slugfest between Mrs Hillary Clinton and Mr Obama until the party's national convention in August, the chairman of her campaign Terry McAuliffe suggested that the race would end quickly after the final primaries next month. 'After June 3, this is going to come to a conclusion,' he said.

Some reports say Mr Obama could wave an olive branch, offering to make Mrs Clinton his running mate.

He has resisted making any direct calls for her to quit and instead has heaped effusive praise on her.

'There's no doubt she's qualified to be vice-president; there's no doubt she's qualified to be president,' he said in a TV interview.

In another, he said: 'She is tireless, she is smart. She is capable. And so obviously she'd be on anybody's shortlist to be a potential vice-presidential candidate.'

He said he had not discussed the issue with her, adding that it would be presumptuous while she was still pursuing the presidency.

'As soon as I know I'm the nominee, then I'm going to start making overtures to her, as well as everybody else, to figure out how we can bring this party together,' he said.

Mrs Clinton, meanwhile, had a less than stellar day on Thursday.

She was accused of playing the race card by equating white people with hard work and blacks with laziness.

She had claimed in an interview with USA Today that she would be the better nominee because a recent poll showed that 'Senator Obama's support among working, hard-working Americans, white Americans, is weakening again'.

The comment stoked fears that she was using race to damage Mr Obama's chances of an election victory and sparked thousands of angry posts on blogs and chatrooms.

Yesterday, she continued to campaign for the upcoming primaries, but the talk has now turned to how she can make a graceful exit from the stage.

bhagya@sph.com.sg