While it's a firm tradition now to have a strong separation of powers in the U.S., there's nothing in the Federal Constitution that requires it of the States. Indeed, at the time that the Constitution was adopted, there were states that had the executive be part of the upper legislative house and/or had their upper house possessing some judicial powers.
Which states?
I'm not going to do an exhaustive list, but New Jersey's had both features. The Governor was a voting member of the upper house (called the Legislative Council) which had one member from each of the thirteen counties plus the governor.
VII. That the Council and Assembly jointly, at their first meeting after each annual election, shall, by a majority of votes, elect some fit person within the Colony, to be Governor for one year, who shall be constant President of the Council, and have a casting vote in their proceedings; and that the Council themselves shall choose a Vice-President who shall act as such in the absence of the Governor.
The Legislative Council also served as the New Jersey supreme court for cases in law, but not in equity.
IX. That the Governor and Council, (seven whereof shall be a quorum) be the Court of Appeals, in the last resort, in all clauses of law, as heretofore; and that they possess the power of granting pardons to criminals, after condemnation, in all cases of treason, felony, or other offences.
New Jersey kept their 1776 constitution until 1844.
