I have made quite a few quilts this way and it always turns out fine in the end...keep going. I am a scrapaholic and cannot bear to throw anything out...but I am overrun by scraps! So I sit down at my sewing machine for a day and sew them all together, just as you described, cutting them down to 6.5 inch blocks. Another day, I'll start sewing the blocks together. The end result is usually a bright, crazy, cute baby quilt, which I then give away.....
My motto....Never THrow Anything Out!