It's true that humanities, in particular, don't generally live on large grants. But what "survival" means for them may look quite different. As large-scale grants are lost elsewhere, administrations will wring what they can out of the programs that live on tuition -- English, History, Foreign languages, etc. -- and that means preserving their high-enrollment general education courses and starving or closing majors, which require advanced courses with low enrollments. This model of humanities/social science areas as service units will atrophy in their research roles and lead to extinction of tenure-line appointments, lower salary scales, and inability to attract promising talent into academic careers in those fields.
This was already underway at many universities before the Trump administration attacks. At the Red State school where I once taught, which Carnegie Classifications ranked as first nationally in the total number of annual arts and humanities doctorates awarded, a politically sensitive administration had already begun this shift away from funding humanities majors with lower enrollment advanced courses and towards a laser-like focus on programs keyed to large-scale grants and state workforce development models (which is important for public universities, sensitive to state political control). If this is the general pattern, then universities will try to ameliorate the Trumpist attacks by shifting as much support to STEM and biomed programs as possible, actively seeking private grant and philanthropic support as well, while simultaneously propping up shortfalls in those areas by draining general funds from humanities and some social sciences.