It's also bad writing. So how long would it take for the Enterprise to cross through the cloud to get to V'ger itself?
If Warp 7 were 7 to the 3rd power times lightspeed (as the old Making of Star Trek implied), and the cloud were standing still, it'd take .99 minutes to go from the outside to the center. If it's coming at you at warp 7, halve that. The film implies a "conic section flight path" which means heading towards the center of the cloud as it passes and then overtaking from behind, so the time it would take really depends on the approach vector (how far off center of the cloud's course) and how fast the cloud was going.