Americans held that virtue was pivotal to the success of their new nation. what did they mean by virtue? how did they hope to ensure that their citizens and their leaders possessed virtue?

By virtue they meant to be  morally correct. And it was guided by religion.

Nevertheless, to provide the real virtue comes from an inner force and should not be imposed. That is how virtue and liberty are tied. To be really free you should choose virtue as result of your own beliefs.

That is what the independence declarataion and the consitutuion promoted liberty and virtue.

Then the laws ant their enforcement were the media to ensure the virtue (and freedom). 

The answer is challenging and taxing because arduous means when something is hard and tiring and the excerpt provides clear detail why that's the answer