There is little surprise in the daily criticism from Republican opponents. But now she has become the target of attacks from Democrats in the state and doubts are growing over whether she will run.
Perhaps it is her worsening polling numbers that are doing it or a recent "poison gas" gaffe committed in the Middle East when she met the wife of Yasser Arafat, the Palestinian leader. Whatever the reasons, figures in the party have variously urged her in recent days to give up her day job as First Lady and get on with running for the Senate seat at full pitch or to jettison her putative candidacy altogether.
Most outspoken has been Ronnie Eldridge, a member of the New York City Council. "Clearly, she is the weakest candidate," she told reporters at the weekend. Noting that Mrs Clinton's expected opponent, the city's Mayor, Rudolph Giuliani, is extending his lead over her in the polls, she urged Mrs Clinton to drop her Senate ambitions and clear the way for another candidate.
"I just think there are too many problems inherent in the campaign," Ms Eldridge said. "Up until now, people have been very hesitant to say that. But the more I talk to people, and the more you hear from people, the more dissatisfaction you hear."
How Mrs Clinton will react to the pressure is uncertain. She has recently been out of the country with the President for the summit of the Organisation for Security and Co-operation in Europe and visits to Greece and Bulgaria.
But any pronouncement of the death of her candidacy would be premature. She and her husband have only recently completed their purchase of a house in a suburb of New York City, a move designed to establish her residency in the state.
"Hillary Clinton has made a commitment to the people of New York and when she makes a commitment, she keeps it," her spokesman, Howard Wolfson, said last week.
In reality, no firm commitment has been made. Neither Mrs Clinton nor Mr Giuliani has formally declared the decision to stand for the seat being vacated by Daniel Patrick Moynihan. Mrs Clinton was not expected to make such a declaration until the new year.
But Carl McCall, the New York State Comptroller and the highest-ranking Democrat in the state, is urging her to "rethink the timetable".
He implored her to move quickly to announce her candidacy, move into her new house and appoint a full-time campaign manager. "All three of those things ought to happen simultaneously and as quickly as possible, like tomorrow," he said.
The polling data have been discouraging for Mrs Clinton. A Siena College survey released last week had Mr Giuliani leading Mrs Clinton by 48 per cent to 36 per cent.
A New York Post poll at the weekend had a majority of state residents saying Mrs Clinton should not even enter the race; 53 per cent of people in the state said she should not run for the Senate, while 45 per cent said she should.
Then there was the brouhaha that followed Mrs Clinton's encounter with Suha Arafat during her solo visit to the Middle East 10 days ago. Mrs Clinton's error was in failing to respond when Mrs Arafat said that for years Israeli forces had been poisoning Palestinians with gas.
Television cameras then watched as the two women embraced. Mrs Clinton only responded to the allegation after Mr Giuliani remarked on the incident back in New York.
"Clearly now, Democrats are beginning to acknowledge what very hopeful Republicans are observing, which is Mrs Clinton doesn't appear to be ready for prime time," Jay Severin, a Republican consultant in New York, observed yesterday.
The Arafat mishap is already costing Mrs Clinton. Television advertisements that will begin running this week, funded by the Republican Jewish Coalition, offer this commentary about Suha Arafat's outburst and Mrs Clinton's silence: "Instead of reacting with outrage, Hillary Clinton sat by silently. When Arafat was finished, Hillary gave her a hug and a kiss."Reuse content