Scrapping tuition fees wouldn't affect the core vote that much. The people who benefit from university education generally go on to have a higher income than average and to come from wealthier families.
The devil is in the detail here. The Tories scrapped means tested, non repayable grants for the 2016 entrants. Restoring those would benefit those who come from poorer families, who tend not to come from families with a history of higher education.
Reducing the cap from the current £9250 to (say) £6000 would help virtually nobody, except the wealthiest. The reason for that is most graduates will never pay back their loans, which are written off after 30 years. It doesn't matter how much is left after the 30 years and the amount doesn't affect the actual repayments.
However, reducing the fees to £6000 would mean that the wealthiest families would probably choose to pay them upfront, which means that there would be no loan repayments. Parents are already paying an average of £20,000pa for independent schools, so university fees are cheap!
Jo Johnson is against scrapping fees, so it will be interesting to see what happens. If they are scrapped, I bet Nick Clegg will be cursing. 
PS. If I had a magic wand and a unicorn, I'd reduce OU fees and restore funding for adult education courses. I'd also put more money into primary education and early years (or, at least stop the cuts), because the damage to a child's life chances has already been done long before university level.