But Mrs Dole's announcement, on a much-prized morning news show, made precisely one paragraph in the next day's Washington Post. It came well after a story about George W Bush, the leading candidate for the nomination, a man who is steamrolling the rest of the party on his apparently unstoppable path to victory next year. It was supposed to be a positive statement, but it ended up looking "as if she was saying, `I still have a pulse'," as one Republican analyst said.
One of Mrs Dole's campaign advisers did get coverage - lots of it - further back in the Post, in the Style section. Jeanne Kirkpatrick, the former Reagan official who wanted America to back Argentina in the Falklands War, was given a hefty piece in the gossip column. She had got into a shouting match with a police officer after someone reported that she had left her dog in the car in 100F heat.
It was not a great week for Mrs Dole, in short. When she announced her interest in the presidency, she got headlines around the world. The idea of a woman candidate sparked huge interest, raising the prospect that America might go down the same road as Britain, Israel, Pakistan and many others, and elect a woman leader.
But Mrs Dole looks as if she could be an early victim of the Austin Strangler, Mr Bush, the Governor of Texas. It was the news of his massive fund-raising prowess that swamped any mention of her in most of the media, as his staff confirmed that he had raised more than $36m (pounds 23m) in the first six months of the year. She has raised about a tenth of that. If money decides elections - and it does - then her prospects are not bright.
But the opinion polls, too, had a grim message for the Dole campaign. Mr Bush has been campaigning only since last month, and he has wiped the floor with Mrs Dole. She was a healthy second in early May. Now Mr Bush has nearly 60 per cent support, and climbing, among Republican voters. "His lead over his closest rival, Elizabeth Dole, has expanded from 32 points earlier this month, to an impressive 51 points today," said Gallup, which carried out the poll. Mrs Dole is now back with three others in a race for silver: Steve Forbes, Dan Quayle and Senator John McCain, all at around 8 per cent. Mr Bush, in every sense, seems to have the gold.
Mrs Dole is trying hard, perhaps too hard. When George W flew into Iowa for the first time last month, he talked in vague ways of "prosperity with a purpose", "compassionate conservatism", and so on. Mrs Dole made a much more precise, drilled performance the same morning - a 10-point plan, in fact. She was a little nervous, and prompted her supporters when they failed to clap at appropriate times. It was all a little too controlled.
Sixty per cent of Republicans believe that it would be better if there were one candidate out in front, removing any uncertainty, and that points, overwhelmingly, to Bush the Younger. But Iowa and New Hampshire, the first states to choose, do not necessarily see things that way: they prefer to think for themselves. "Are we witnessing the buying of the presidency? It sure looks that way," said the Manchester Union Leader in an editorial last week, reflecting the New Hampshire paper's harsh view of Mr Bush. He has a smaller lead in Iowa than nationally, with 40 per cent of Republican voters, according to a poll in the Des Moines Register. Mrs Dole is second again, and still well back, but just clear of the pack with 13 per cent. Breathing down her neck is Steve Forbes, with 10 per cent.
Mr Forbes is a billionaire, his fortune founded on his father's media empire. He will certainly still be there next year. Mr McCain is not targeting Iowa, and he won't do well. The other conservative candidates - Dan Quayle et al - may drop out by the end of the year as the money crunch hits them. So things are not quite as bleak as they look.
The conventional wisdom in the Republican Party is that there are three primaries: one to win the nomination, one to represent the conservative vote and one as the moderate back-up in case the Texas Tornado blows himself out. Mrs Dole is fighting for the last slot, and her main competition is Senator McCain. The latter has made good headway, getting headlines both for his stand on Kosovo and his calls for reforms to the system of campaign finance that has allowed Mr Bush to get so far ahead. Mrs Dole has had no shortage of policies - last week she called for filtering the internet to remove pornography - but they have not hit the headlines in quite the same way.
And it is here that her supporters can justifiably blame the media for a male bias. Mr McCain's ideas are much more in tune with the Washington news agenda, centred on hard, traditional issues, and he gets the plaudits. Mrs Dole's ideas are aimed very much at the suburban families who will be such a crucial part of the electorate next year - against pornography, drugs, even guns - and they resonate. Three quarters of her support comes from women.
But then maybe the old Texas political proverb is right: there ain't nothing in the middle of the road but white lines and dead armadillos.