Kristin, with the limited information you've provided it's not possible to provide you with much help.The first and rather vital question would be on what basis do you believe that Josiah Churchill was your husband's "Churchill colonial ancestor?"There are five American Churchill families that date back to colonial times.You presumably must have some documented line of descent to know that your husband is a descendant of Josiah.As the genealogy of the three northern American Churchill families is well known through the 1904 book "Churchill Family in America," that obviously provides a starting point for researching any connection to your husband's Spencer ancestors.
Incidentally, to correct a couple of points, Josiah's place and date of birth have never been established.He probably died on January 1, 1687, not 1686, and he would have been buried in Wethersfield, where he lived and died, not in Newington, which was only just beginning to be settled and was not yet even established as a separate jurisdiction in 1687.
As to the name Spencer, are you referring to American Spencers or to the English Spencers of which the Winston Churchills are a part?If you are referring to the English Spencers, there is no connection that I'm aware of to the Josiah Churchill line.There certainly is no connection to the Winston Churchill line, which many American Churchills have erroneously sought to claim.
Of course, Josiah has innumberable descendants bearning any number of family names, so there certainly could be a Spencer among them.But from your reference to "bogus links to famous English peers" I gather you have something more specific in mind.