Question: Did they like Oliver Cromwell, who founded a republic after a dispute about taxes led to the overthrow of a king, or did they see him as a usurping Caesar who destroyed a republic and became a tyrant?

Answer: 
No.

On the one side, we have Hamilton denouncing Cromwell in the [Federalist Papers No. 21](http://avalon.law.yale.edu/18th_century/fed21.asp):

> 
> Without a guaranty the assistance to be derived from the Union in
>  repelling those domestic dangers which may sometimes threaten the
>  existence of the State constitutions, must be renounced. Usurpation
>  may rear its crest in each State, and trample upon the liberties of
>  the people, while the national government could legally do nothing
>  more than behold its encroachments with indignation and regret. A
>  successful faction may erect a tyranny on the ruins of order and law,
>  while no succor could constitutionally be afforded by the Union to the
>  friends and supporters of the government. The tempestuous situation
>  from which Massachusetts has scarcely emerged, evinces that dangers of
>  this kind are not merely speculative. Who can determine what might
>  have been the issue of her late convulsions, if the malcontents had
>  been headed by a Caesar or by a Cromwell? Who can predict what effect
>  a despotism, established in Massachusetts, would have upon the
>  liberties of New Hampshire or Rhode Island, of Connecticut or New
>  York?
> 
> 
> 

And from the other side, the [anti-federalist Brutus papers](http://www.constitution.org/afp/brutus10.htm):

> 
> I firmly believe, no country in the world had ever a more patriotic
>  army, than the one which so ably served this country, in the late war.
> 
> 
> But had the General who commanded them, been possessed of the spirit
>  of a Julius Cesar or a Cromwell, the liberties of this country, had in
>  all probability, terminated with the war; or had they been maintained,
>  might have cost more blood and treasure, than was expended in the
>  conflict with Great-Britain.
> 
> 
> 

So "Cromwell" is a term of abuse equivalent to "Caesar" for both sides. The answer to your question may be different if you asked if early New England colonists saw Cromwell as a role model. But keep in mind that the [southern gentry saw themselves as cavaliers](http://en.wikipedia.org/wiki/American_gentry)--they would have detested Cromwell. And Americans in this period venerated [Cincinnatus](http://en.wikipedia.org/wiki/Lucius_Quinctius_Cincinnatus#Legacy), who is effectively the anti-Cromwell.
I do think that the fact that Cromwell's sect of Puritans mostly emigrating to Massachusetts is part of the reason that the first shots of the revolution were fired there. There must have been, only a few generations later, a seething dislike of the crown. Think about supper table talk. No doubt that many were the grandchildren of people that fought in Cromwell's campaigns. Sympathy for Cromwell and his attitudes had to be present.