Consider opportunity for better IA:
Instead of just thinking how one could show 150 or even 50 menus on mobile page, I think first of all the efforts should be directed for better information architecture.
Ideally it should be identified by users (Card sorting) but at some level (considering experience and domain knowledge) designer and stakeholders can think of logical groups.
Grouping and Chunking should help:
There might be possibility for better organizing menus in some logical groups. Also if this website already exists, one can also see which are the important menus from users point of view; AND/OR which menus are frequently used; so that those can be pushed upfront for users.
Scrolling is definitely not going to help:
Though its said that these days users are not much concerned about scrolling, it DOES depend upon the type of content. For Facebook, its OK to let user scroll to see engaging, contextual and live (constantly changing) content. In contrast, here we are talking about static menus which will rarely change. In fact user will be looking for only those which will direct him towards expected content.
Auto Suggestive search box:
If at all, its not possible to reduce or group menus as mentioned above; One way to help user go to particular menu can be using Auto suggestive search (what Google does for their search) Here the bottleneck is that user has to know or at least guess the menu, so that while typing, related options can be shown and user can select the one which he wants. Though this is not the best option, it will definitely reduce users motor workload i.e. scrolling and visual load of searching while scrolling.