While human brains are more complex in many ways than our most advanced modern computers, there is no scientifically justifiable reason to think that anything a human can do is simply impossible for a sufficiently advanced computer. We don't know exactly how long it's going to take, as we don't fully understand the human brain, but based on our advances to date we can get an idea that it could well be within 50 years that we get a a very interesting two-way conversational AI.
What helps this is that the human brain is not 100% for conversation. Much of the brain is used for every other thing a human does, from sight and hearing to movement to keeping us from falling over dead. While it should logically take far longer to replicate a human brain, there is no reason we we can't have various degrees of intelligence and behaviors far sooner than what it would take to have the first fully artificially created human brain equivalent device.
Indeed, in many ways we already have recreated many otherwise "human only" or even "beyond human" abilities. We have computers that can recognize faces even across dozens of years of aging, translate human language with some facility, navigate through 3D space, and many other highly difficult tasks - like winning on Jeopardy or at Chess.
The trick is that we don't have computer systems that can do all of that at once, weaving them all together seamlessly. That's just too much for our present level of development, and there's still plenty of things humans can do intellectually that have no equivalent computer expression. Some things we just haven't figured out, and may not figure out for many, many years.
Now, if you consider intelligence as the full range of human intellectual ability, that's going to take a whole lot of advancement. But if you accept the concept of "materialism" (the philosophy, not the "I love owning stuff" concept) as opposed to something like "dualism", then it's just a matter of time. If there is no magic pixie dust that makes humans intelligent, there's no reason a silicon-based thing can't be developed to have equal or greater intelligence.
How long is that going to take? Beats the heck out of me! It's not possible to know, because we don't know how hard the problems are to solve until we've pretty much solved them.