It sounds like there are 2 potential issues here. (1) Problem with bandwidth settings and (2) Possible issue with package deployment using task.
I have a few questions that could help us troubleshoot this:
0) What version + Service pack version of SMP are you running?
....And are your managed clients using the corresponding Agent version?
1) Do you have Bandwidth Throttling enabled in the targeted agent settings policy?
...Can be accessed under Settings -> Agents/Plug-ins -> Targeted Agent settings
2) When you attempt to push using a quick delivery task, do the agent logs show the same message as when you try the Managed delivery job?
3) Are there any errors/warnings on the NS side when you try the quick delivery method?
4) Do any of the computers you are pushing to have multiple NICs?
5) Do the target client machines have relatively slow WAN links?