How do I unfreeze my gutters?

I live in Michigan and have a heat strip across my roof ledge off the back door and down into my gutters and down-spout so that melting snow will drain (there is no soffet vent). Its worked great but a couple weeks ago the heat strip died. Now the heat strip is frozen to the roof and I have a huge amount of ice in my gutters to where its overflowing. I tried roof melt pucks but the ice is too thick and won't budge. How do I get rid of the ice in the gutters?