Is it acceptable to propose the same PhD research plan to two universities?
Chances are that your supervisor at the first university is sensitive to the challenges in acquiring funding. If you have been clear to him/her that you cannot pursue the studies without support and are solely dependent on external funding, then he/she should certainly understand if you pursue them elsewhere where funding is available. Furthermore, if you are up front about it, the supervisor may scramble more to find funding for you. The situation is not unlike courting two potential employers during a job search.

I would not recommend suggesting to the second supervisor that he/she is a backup option, but only that you have also applied with a warm reception to the first university. This way, you do not risk stepping on egos, but still make it clear that you are entertaining other options.