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.
Extemely short and simple answer: No, because for one thing, Cromwell eventually set himself up as dictator, the "Lord-Protector", which was simply a title for the person in charge. He first created a non-elected "representative" system before that, where the people in that system were simply nominated but not elected. In other words, he was very much like a Caesar, which started out with having a "Parliament" that he effectively controlled. The person(s) above goes into more detail, but that pretty much sums up why they wouldn't have a positive view of him. That said, ironically, one person who did have a positive view of him was Karl Marx, who viewed him as an early revolutionary.