The Moon already keeps one face to us. Given long enough the Earth would do the same back, and a day and a month would both be about 47 of our present days.

Tides are slowing the Earth and widening the Moon's orbit, and the process only stops when both rotations match the orbit. The arithmetic says it would take something like fifty billion years, which is more time than the Sun has: it will swell into a red giant in about five, and the question becomes academic.