Barack Obama has set up a small team of trusted advisers to begin the search for a vice-presidential running-mate, amid reports that Bill Clinton is pushing hard for his wife to be given the role.

Mr Obama has asked Jim Johnson, the former head of the government-run mortgage lending giant Fannie Mae, to begin the vetting process, and has sworn a group of his closest advisers to secrecy as a shortlist is drawn up. Mr Johnson handled the same assignment for John Kerry in 2004 and Walter Mondale in 1984.

The move comes as John McCain, the Republican nominee-elect, has invited three possible running-mates to his Arizona ranch this weekend: Mitt Romney, a former Republican rival for the White House nomination; Charlie Crist, the popular Republican Governor of Florida, and Bobby Jindal, 36, the newly elected Louisiana Governor and a rising star in the party.

Mr Obama, aware that he risks alienating Mrs Clinton’s supporters further if he acts as though he has already beaten her, said: “I am not commenting on vice-presidential matters because I have not won this nomination.”

Yet with the prize now within his reach, sources inside the Obama camp said that some members of the Clinton campaign were lobbying for the former First Lady to be Mr Obama’s running- mate. According to one report yesterday, Mr Clinton believes that his wife has earned the vice-presidential slot, and “is pushing real hard for this to happen”.

It is unclear what Mrs Clinton thinks, and less certain that Mr Obama would offer her the position. Although many Democratic voters see it as the “dream ticket” to unify the party, having her as his running-mate would run counter to his message of generational change.

Meanwhile, Mr McCain has hinted at a line of attack against Mr Obama in a general election. He derided the Democrat last night for his lack of military service. The Illinois senator responded by criticising the Republican’s “endless diatribes and schoolyard taunts”.

The exchange was triggered by a Senate vote over a Bill extending educational benefits for veterans. Mr McCain, a former Naval pilot and Vietnam prisoner of war, opposed the legislation because he thought that it could encourage military personnel to leave early. Mr Obama supported the measure, which passed easily.

After being criticised by Mr Obama for opposing it, Mr McCain said: “I will not accept from Senator Obama, who did not feel it was his responsibility to serve our country in uniform, any lectures on my regard for those who did.”

Back on the campaign trail, Mr Obama continued lavishing attention on Florida, to heal a rift that could cost him the state in November. Along with Michigan, it was stripped of its delegates for flouting party rules by holding its primary too early.

Mrs Clinton, who won both disputed contests, will push at a critical meeting of the Democratic Party’s Rules and Bylaws Committee next week to have both states’ delegates added to the total. Mr Obama said that he would agree to half the delegates being counted. Last night Florida’s Democratic Senate majority leader sued the national party to have all the delegetes seated, a move that helps Mrs Clinton by keeping the issue alive.

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