I can't tell what the sentence is talking about, and when you can't tell what the sentence is talking about, it's a dead giveaway that it's a fragment.
The basic meaning of willing is, "an expression of desire and consent."
Here, the words, "As I see it we can have no new deal until" convey Eleanor Roosevelt's appeal for cooperation and participation to women and other groups.
She means that we cannot move forward without the cooperation of intelligent, hard-working and determined women who decide to take part in matters of the country.
