Set the input field size attribute (if not already set) based on an estimate: the length of a formatted date (e.g. today's date). This could be disabled with a flag in the settings (e.g. autosize=true/false).

A working implementation: add the following two lines to _connectDatepicker:

if (this._get(inst, 'autosize') && !input.attr('size'))

input.attr('size', this.formatDate(this._get(inst, 'dateFormat'), new Date(), this._getFormatConfig(inst)).length);