Obtuse means greater than 90 but less that 180 degrees.

The angles in a quadrilateral sum to 360 degrees. There must be 4 angles in a quadrilateral.

take a square: 90 + 90 + 90 + 90 = 360

for all of these angles to be obtuse they'd have to be at least 91 degrees.

91 + 91 + 91 + 91 = 364

Therefore, my answer is no.

Hope this helps :)