No, there is no way to do that while draging the clips
But there's a trick to do it. First, turn off "Snap to Grid" (key N) in track view. Select the clip, Press Ctrl and <-- or --> to zoom. By zooming the clip wider, you can drag-and-drop in more precission. Use the mouse to drag the clip.
Or...
Select the clip, right click, Clip Properties... and put a new start value in the field. Click Ok. That's it... precission
4ever, There's also a trick to make the sound more "full". Record a track mono. Clone so you have now two identical audio track. Click Process --> Audio effects --> Cakewalk --> Time / Pitch scretch. You only have to decrease the pitch by -0.20 applied to the second track. Done ? Good... now play 'em both

Wiiide...
That's cool, but I need wider, Jaymz
Pan them hard L & Hard R.
Okay... but I said I realy need it wider and fatter, Jaymz
Okay... clone the original track once again. So you have total three track. Let the first track alone, centered. The second is decreased -0.20 pitch. Pan it hard left. Third track is increased +0.20 pitch. Pan it hard right. Adjust the second & third volume level compared to the first track. Play 'em together
FYI, small amount of altered pitch won't screw the sound, instead, it gives you "fat" sound effect (chorusing). Combined with delay effect Paul mentioned, you'll get the ticket to next Grammy award for wider & fatter record
Hope it helps

Jaymz