A lot of people have expressed that sentiment either on the Internet, or in articles, or in person. Such people claim that it's not Clinton's gender that bothers them, it is her personality. They don't trust her, think that she is insincere, and are supporting Obama in the 2008 race for the Democratic nomination. The sentiment that Clinton shouldn't be elected is often expressed by Democratic women in their 40s and 50s. Such women seem to assume that there will be an opportunity in the near future to nominate and elect a Democratic woman as president.
They shouldn't be so sure. In 1928, the Democratic Party nominated the first Roman Catholic, Al Smith, for President. He was defeated. It was another 32 years before another Roman Catholic, John F. Kennedy, was nominated and there has not been a Roman Catholic nominated by the Democratic Party or the Republican Party since 1960. This in spite of the fact that Roman Catholics are a highly prized voting block by both political parties.
In 1984 then New York Senator Geraldine Ferraro was selected for Vice-President by Walter Mondale. Now, 20 years later, Hillary Clinton is running for president. That means that two decades have passed since Ferraro was on the ticket and she wasn't chosen by voters but rather by the Presidential Democratic nominee.
Hillary Clinton possess several advantages that most women politicians don't possess. She has great name recognition, can raise money, is Senator from a big state that is home to a lot of big media companies, and has a husband who is a former president. She is the best positioned woman to run for president in the history of the Democratic Party. If she doesn't make it, it will be years, possibly a great many years, before another woman is in such a position.
All that is not to say that women voters who like Obama shouldn't vote for him, or should support Clinton just because she is a woman. What I am saying is that people who support the idea of a woman president, but vote against Clinton, should realize that they might not another opportunity in their lifetimes.