A senior Tory says the views expressed by the leadership rivals appear to rule out any compromise.
The government says it will bring better support for victims, but charities warn more funding is key.
The environment secretary says both Boris Johnson and Jeremy Hunt "would do a great job".
German Ursula von der Leyen will replace Jean-Claude Juncker on 1 November after a close vote.
It would help parents share childcare and businesses keep staff, Tory MP Helen Whately says.