It is entirely possible that two groups of creatures can be able to breed together just fine. But, they don't want to. That situation is not stable. Eventually the two groups must diverge, by natural selection or perhaps simply by neutral drift of their gene pool.
If that situation represents a speciation about to become final, then there should be less extreme situations: speciations that are still underway. A recently published example are the passion-vine butterflies Heliconius erato and Heliconius himera.
H. himera lives in dry thorn-scrub habitats of Andean valleys. It is considered to be a race of H. erato, rather than a separate species. The two are geographically separate: the dividing line between them is the boundary between dry and wet forest.
In a lab setting, the two interbreed with perfectly normal success. But, given a choice, each will breed within its group about ten times as often as they will breed with a member of the other group.