A software tester should run behind on Time or Test coverage..?

If bug count increases means mutually the time line get increase.
We can not predict what is actually happening in the software before start the test ( may you have get bunch of documents to understand the functionality of the software, but after read those things you can assume the work flow of the software but not able to assure the things which you had read it in documents absolutely in the application.,
So it is impossible to set time line to accomplish test coverage of the application right..? But in practical, every software tester(i hope) test the application with the time line.,
Is in it possible to meet test coverage in estimated time line..? If a tester works based on time means, what will happen to the quality of the application, because now tester concern about the time line not about the quality.., (to be continue :) )