My conclusion after reading the Pew Research Study on Judaism in America is that liberal Judaism slows assimilation, but cannot stop it. However, that doesn't strengthen the notion of Orthodox Judaism as the only hope for the survival of American Judaism. If Orthodox Judaism became the only Judaism in America, more people would just stop being Jewish immediately.
My biggest issues with Orthodox Judaism are its stances on women and homosexuality. These are non starters for me. Liberal Jewish movements have to make their synagogues more welcoming, engaging, relevant and educationally sound.
I believe that hospitality is the key to bringing people into a community, and this is not a strength of many liberal synagogues which are too centered on their buildings and institutional values rather than on the people who do and could potentially go there. The first Jewish guy, Abraham, was hospitable to the 3 "visitors" even though he was super old and had just been circumcised. Open your tent, be welcoming, and people will come.
Will their children? If they can find another hospitable tent, I think so.