When does admission to major after enrolling become a concern?

At what level of competitiveness or GPA/grade threshold would you be concerned about a student not being able to do his/her desired major at the college?

More of this – an example would be a student who would be capable of completing the desired major with (for example) a 3.0-3.3 college GPA, but is weeded out of the major or not allowed in because the minimum college GPA was (for example) 3.5 to get into or stay in the major.

More concrete example: if a student who wants to major in CS were admitted undeclared to Washington, UIUC, and/or UCSD, would you recommend that s/he attend one of those schools (assuming no other things like cost prevents it), or would you recommend that s/he more strongly consider other options where getting into the CS major is less competitive?