I don't think the answer she gave actually changed anything regarding her confirmation. The same people who were going to vote for her still voted for her, and the same people who were going to vote against her still voted against.
The smartest thing to do as a Supreme Court nominee is to say as little as possible that could ruffle anyone's feathers.
In that particular no, it didn't change much as in the Senate, the Democrats at the time had those "brute force" numbers I referred to. (the same way the republicans have been getting their nominations through this time)
The implications aren't always just for the nominee's own confirmation and their personal career advancement, but sometimes for the trajectory of the person/administration that appointed them.
If there's a policy/position where 70% of the population (overall) is leaning one particular way, a nominee either clearly dodging (or going the other way), can have impacts on the future re-electability of the person who appointed them, as it can be an indicator that perhaps they're moving too far in a direction that the majority of people aren't comfortable with. Likewise, if a policy is overwhelmingly popular with their own party, but they give a wishy-washy answer in hopes of giving enough appeasement to the other side to get more senate votes, that sends a signal as well.
In her case, the answer she gave didn't appease republicans, and it didn't appease the progressive wing of the democratic party.
We know their respective answers to that question
GOP: "It's an adult human female, case closed, no further discussion, no room for nuance"
Progressive wing: "It's anyone who identifies as a woman" (typically followed by some sort of rhetorical "how do you define a chair?" trick they learned in Philosophy 101)
