The umbrella body says such a decision would have to be approved by both the House of Commons and the Lords. Usually, that would be done in a delegated legislation committee, which has a limited number of members.
But the NCVO hopes to pressure the Government into letting all MPs and peers vote on the issue on the floor of each house.
"I think we've got a strong case to say it should be debated on the floor," said Pete Moorey, parliamentary and media manager at the NCVO.
Jowell is expected to make an announcement in June about how the Government expects to finance the rising costs of the London Olympics.