The short answer is no.
I clearly need to spend more time on this subject but what's already there will return something like:
Seq(1, 2, 3) must haveAllElementsLike(e => e must beGreaterThan(3))
> in 'Seq(1, 2, 3)'
some elements are not correct:
1 is not greater than 3
2 is not greater than 3
I deliberately changed your example because the hamcrest method "hasItems" is ambiguous IMHO. It takes a list of matchers and apply an OR to them but it's so clear from the name, it could be AND as well.
Then I think that a full failure message is better than just a description of the matcher because you also get the actual value that has been checked, not only the expected one.
Anyway there is certainly some room to improve existing collection matchers (you're the second person to ask about that in the last 2 days :-)), I'll try to look into this and learn from Hamcrest.
E.