Canuck, you are incorrect. The comma announces that a quotation of dialogue is coming up, and the first letter of the sentence spoken by the speaker is to be capitalized, unless you are quoting only part of the sentence, in which case an ellipsis is used to indicate there are words missing from the sentence. Go pick up any published book and find some place where <He said, "The sun is shining"> doesn't have the word "the" capitalized. On the other hand <He said that the sun was shining> has neither mid-sentence capital nor comma because he is not being quoted.
<She said it was a "cute dress"> does not require capitalization of "cute" because there is no sentence within the quotation marks and all the quotation marks do is establish that "cute dress" were the words she spoke, and that she didn't say it was "cutesy" or some other word, but she actually said "cute dress."
It has to do with whether you are quoting the dialogue: She said, "Cute dress. How much did that cost?" or quoting FROM the dialogue: She said the dress was "cute" and asked, "How much did that cost?" Note that there is no comma in front of "cute" but there is in front of the quoted question.
The comma is really a critical component to designating whether you are quoting the entirety of what was said or only a specific word or phrase out of the entire sentence. OP's original example was this: When I laid the bag on the counter, Amy said, "that's cute."
Had she instead written, "When I laid the bag on the counter, Amy said it was "cute,"" then you have a different situation. But there is no comma after "Amy said" now and that makes all the difference.
<Amy said it was "cute"> and <Amy said, "It was cute."> are two different sentences. In the first case Amy might have actually said, "You may think it made you look fat but I thought it was cute." In the second case, Amy just said, "It was cute," without speculation about what the wearer thought.
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I pray it does not occur that the last thing I did before I died was vacuum the house or eat broccoli.