MailChimp recently started to force the use of "API Key" for API authentication. They want you to use the API Key option rather than the normal "username" and "password" option for API authentication.
eStore and affiliate had the "API Key" option already built in. We have updated the eMember plugin so that an API Key can be specified in the settings for this plugin too. Get a new build of the plugin(s) from here and you will see the API Key option in the settings:
http://support.tipsandtricks-hq.com/update-request
Basically, get the API key from your MailChimp account and use it in the "API Key" field of the autoresponder settings of the plugin and the plugin will use that.