What is the Biblical basis that God "cannot" act against his nature? I understand the traditional theology of omnipotence to be that God can do anything He wills, and that his omnipotence is thereby limited to His nature.  In other words, saying that God can do anything does not imply that He can lie or sin.   For example:


  God is all-powerful and able to do whatever he wills. Since his will is limited by his nature, God can do everything that is in harmony with his perfections. – Thiessen 


The best proof texts for this seem to be Hebrews 6:18 and 2 Timothy 2:13. 
However, based on a debate with a friend, I asked this question on Biblical Hermeneutics SE, and got an answer that surprised me: 

According to the answer, Hebrews 6:18 does not necessarily mean that God cannot lie - only that He won't.

So this leads me to a question: What is the Biblical basis for the doctrine that God's omnipotence means that he cannot act against his nature?  Would it perhaps be more correct to say that he will not act against his nature?
The Concise Oxford English Dictionary (11th ed.) defines "nature" as "the basic or inherent features, qualities, or character of a person or thing."

For God to act against His nature would mean, employing the COED definition of "nature", that He would be exhibiting features, quality, or character that were not basic or inherent to Him.  In essence, He would change.

Scripture teaches that God does not change.  According to James, there is no variableness nor shadow of turning in God (James 1:17).  The Lord said to Malachi (3:6), For I am the Lord, I change not.