Interesting thread.
Firstly, what unifies feminism, I think, is the belief that there are systematic injustices or inequalities in society which disadvantage women, and that all feminism wants to address that, albeit in different ways (though I am not sure if this applies to 'choice' feminism, but that is a different debate).
My understanding of liberal feminism is in the tradition of Liberal thought, dating from the Enlightenment, namely the belief that men were rational beings, and that if women gained equal rights to education and employment (i.e. also became rational beings disassociated from the body and nature, seen as feminine in the context of the time), then inequalities would be addressed. Given the emphasis in the liberal tradition on individuality, with the state taking a limited role, the success or failure of individual women within the system (i.e. to gain an education or a job, once barriers had been removed) was seen as a personal responsibility.
I think this comes unstuck when you consider the fact that despite equal pay legislation and more women in universities in certain areas, there is still a gender pay gap, this shows that it is not only a case of removing barriers and legislating for equality, something else is at play.
In terms of the backlash, I feel that is definitely happening now, though the OP may have meant third wave feminism. Take for example, the reductions in childcare tax credit, which will impact on working women, that is directly compromising gains made in the workplace enabling women (and it is mostly women) to juggle work and families. That is just one example. The problem for liberal feminism is defining this as a feminist issue, when there is the language of austerity defining public life, and hard fought rights are being rolled back generally (e.g. access to higher education - call me a cynic, but how long is it before families start making the decision to send sons to uni, but not daughters, given the bill?).