*I understand the US and UK movements weren't the same, so feel free to only address one or the other.
Did most women at the time quietly agree with women's suffrage, but were afraid to speak up (or unable to), or had most of them, to a varying degree, internalized their oppression, and looked at suffragettes as "extreme"?
Or said in a different way: Was there any significant opposition to the suffragettes from other women?
In the US, there were several groups of woman who were opposed to women's suffrage. One of the largest groups was called the National Association Opposed to Women's Suffrage, founded by Josephine Dodge. Most of the leaders of these groups were not average women though, usually upper class. In the Northern US, upper class women against suffrage claimed that voting would interfere with community work done by women, women did not care about voting, women would just vote the same as their husband therefore not affecting the election, or that it would pit women and men against each other.
Here is a pamphlet made by the National Association Opposed to Women's Suffrage, it's interesting to see how regular household cleaning tips are mixed in with anti suffrage propaganda
http://jwa.org/media/pamphlet-distributed-by-national-association-opposed-to-woman-suffrage
And here is an interesting article about the percentage of women who voted during one of the first elections where women had the right to vote in Chicago, and some of the reasons the women who didn't vote gave for not voting.