sewing question

[drowningmermaid.livejournal.com]

I'm making a taggie blanket for a family friend's little man.

I'm trimming it with ribbon to cover where I sewed the tags on.
Problem is, where I'm finishing off the ribbons at the ends, it's bulky. I've trimmed down as much as I can so it's as small as possible without the ribbons eventually fraying, so my question is this:

how am I supposed to fit it into my sewing machine? And will my needle even be able to handle it?



the layers go like this:
ribbon (doubled over)
fusible webbing (that's already been ironed on)
fleece blanket
fusible webbing
ribbon

and it's a little stiff.




I just don't want to break my needle or jam up my machine or ruin this blanket. It's taken me quite a while to get to where I am with it and would hate to have to start over.

Advice please?