As for the Ivy League schools, they usually provide scholarships to any student who doesnt have a good annual family income. But they sometimes reject even students with A*s and scores as high as 2300 (you will need to go for the optional essay too). And then there's extra curriculars and the interview which count a lot too so there r chances but they r few.
But for all I know, many unis there have a minimum criteria of C, whether scholarship or no scholarship.
Now it depends on the kind of programme you want to go for as well. If it's a course which has loads of other competitors aiming for it it will be tough to get one.