Actually, King George III didn't refuse to pass any laws. All the acts passed by Parliament during his reign received Royal Assent.
The truth is that the last time a British monarch withheld Royal Assent from a Parliamentary Bill was Queen Anne and the Scotch Militia Bill [sic]. She withheld Royal Assent on 11 March 1708, more than half a century before George III came to the throne.
For context, in 1766, Parliament had passed the Declaratory Act, stating the colonies were subordinate to Parliament and subject to British Law. That, coupled with a number of tax laws passed by Parliament (beginning with the Sugar Act of 1764 and the Stamp Act of 1765 followed by further acts after 1766) fuelled the colonists' grievances, and led to claims of “no taxation without representation!”.
In 1775, the Second Continental Congress issued the Olive Branch Petition as an attempt to reach a compromise. I think Jefferson's argument in this section of the Declaration of Independence is actually a reference to the king's rejection of that petition.
Now, although it is true that the king had rejected the petition, Parliament had not yet debated it, so there had not been any chance for Parliament to formulate a law, let alone for the king to give Royal Assent. Before that debate could happen however, the petition was fatally undermined in the minds of the British public and Parliament by a captured letter from John Adams (who had been a signatory of the Olive Branch Petition, but who argued in favour of rebellion in the captured letter).