Unit and Integration testing are two very different things, and what constitutes "acceptable" depends entirely on your organisation. It may very well be acceptable to test the system, rather than each unit separately.
Personally, I'm not a fan of automated unit testing, since the vast majority of issues I encounter are the sort of things that only ever come to light in the context of a system test.
I tend to develop incrementally, so that as what I'm working on grows, it becomes its own test harness, and foundations are proved to be solid before building anything on them.
I'd love to be able to automate system testing. It reveals all the things I would never have thought of in a million years of writing unit tests.