I ran into the same issue, and it was a result of the shipping state input being disabled so that the select box was was visible, but the check to see whether to get the value of the input or select box didn’t take into account the disabled property on the input.
If you change line 56 in wp-content/plugins/wp-e-commerce/wpsc-core/js/wp-e-commerce.js to the following, it should fix your problem:
if( billing_state_input.length && ! billing_state_input.hasClass('intra-field-label') && ! billing_state_input.attr('disabled') ){
