The source code for blockchain.info is open-source and has been (and continues to be) reviewed by educated programmers for weaknesses and exploits. From that review, nobody has seen any indication that the password is ever sent out over the internet. It appears to be held within the browser for any purpose where it is needed. There is a browser plug-in that can notify you if the code changes in such a way as to send your password to blockchain.info.
What is more worrisome is that if a government subsidized mining (especially after the debasement declines significantly in another 4 - 8 years), if the other miners thus found it non-profitable, the government could see where every transaction was originating from and going to on an IP basis (assuming not relayed through non-mining peers) and put the information together to track everything and the tax man cometh after those who are not reporting, etc....