The Republican National Committee, it emerged, has ordered its research department to direct as much attention to Mr Bradley, a former basketball star and a senator from New Jersey, as to Vice-President Al Gore - the favourite for the Democratic nomination for next year's presidential race.
Asked for his response to the Republican move, Mr Bradley said: "What's new? I don't really care what the Republican National Committee does." Alluding to the fact that he will only face the Republican party machine if he can somehow wrest the Democratic nomination from Mr Gore, he added: "I'd just love to have the opportunity where it became relevant."
Most opinion polls show a 20-point gap between Mr Gore and Mr Bradley. Public recognition of Mr Gore is high by virtue of his political pedigree. Mr Bradley only started national campaigning at the start of the year, after retiring from the Senate.
The Republicans' decision to focus on Mr Bradley as much as on Mr Gore reflects their own internal polling which shows the gap between the two narrowing and anti-Gore sentiment on the rise.
The proposal to direct resources equally between the Democratic candidates came from the Republican National Committee's director of political and government affairs, David Israelite, who said: "Based on the most recent confirmation of what our internal research has indicated, I've directed our research department to shift its focus to Bill Bradley a full 50 per cent. We will continue to monitor the situation."
"Agreed. Do it!" the committee chairman, Jim Nicholson, wrote back.
Another interpretation of the leaked memo suggested that it could be part of a Republican strategy to play down and demoralise the Gore camp, which remains the chief threat to the Republicans' chances of recapturing the White House. Although the Republicans' favourite, George W Bush, has maintained a 15-point lead over Mr Gore in opinion polls, Mr Gore is likely to have the Democratic party machine on his side and the backing of Bill Clinton - so long as there is no catastrophe in Kosovo.
However, the possibility that Mr Bradley could sneak up on him is increasingly being mentioned, not only by reporters hoping for a real contest, but by Gore supporters looking over their shoulders. Mr Bradley's fund-raising has been much more successful than expected and he has attracted backers from diverse fields, including Wall Street, moderate congressional Republicans and the basketball star Michael Jordan.
Mr Bradley's name is well known across America from his illustrious career as a professional basketball player. He was on the circuit for 10 years after captaining the gold medal-winning US team at the 1964 Tokyo Olympics. He has subsequently written four books, held two professorships and was highly respected as a senator, where he built up a reputation for integrity. It is this quality, and his concern for social and civil values, which he is presenting as the key elements in his campaign.Reuse content