“To ‘fall from grace’ means to sin so badly that there’s no forgiveness big enough to cover it.”

Not at all. The term, “fallen from grace” comes from Paul’s admonition to the Galatians to resist being put under the Law of Moses.

You who are trying to be justified by the law have been alienated from Christ; you have fallen away from grace. Galatians 5:4

Anyone who tries to be justified by the Law is relying on the Law and not grace.  You can’t have it both ways—the Law or Jesus. So, to “fall from grace” is to seek God’s approval by attempting to live up to the Law—even following the Ten Commandments. Such behavior results in being “alienated from Christ,” a serious matter. Paul quoted Deuteronomy (27:26) in saying that anyone who tries such a thing is under a curse because they then have to keep every one of the 613 parts of the Law (which, in fact, has been impossible since 70 AD when the Jewish Temple was destroyed by the Romans—a vast number of the requirements involve Temple/Tabernacle worship).

“Cursed is everyone who does not continue to do everything written in the Book of the Law.” Galatians 3:10

For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it. James 2:10

In no way should this be confused with obeying Jesus’ teachings. Many people mistakenly believe that since we are “under grace,” to expect anyone to be obedient to Jesus’ teachings is to put them under “a bunch of rules and regulations” and is “works righteousness.”