The EFF is already the most reliable org fighting for our digital arms. As far as comparison to the NRA, I suggest GOA[1] is a better model. The NRA is only a fair weather friend of the 2nd.
The EFF is probably as good as it gets for digital privacy issues, unless it becomes a widespread concern for millenials.[1] When you're a small minority like digital privacy activists are, using the legal system instead of the ballot box is your proper recourse, by design. Money would help, somewhat, too, but I'm not sure the tech companies with deep pockets actually support the digital privacy agenda in more than a tepid way.
[1] Which I doubt. Eventually, you'll have millenial senators. But I am guessing they will still care more about terrorism, chinese hacking, etc, than electronic privacy.
Somewhat perversely, Chinese hacking largely _is_ a privacy issue, just not individual privacy. The reason why Chinese hackers in particular are of concern is (1) they seem to engage in substantially higher levels of corporate espionage and (2) are outside of jurisdictions where such things can be appropriately disincentivised / punished [Although there are some signs China might start playing ball as they develop more domestic proprietary information].
There's a data science hurdle -- can e.g. the Russian mob filter though mass hacked email and facebook accounts to find blackmail material that has reasonably good returns with minimal personal time investment -- before the two become one and the same. If we end the decade before we have public conversations about (modulo details) an email from yourself saying 'send money here or we will forward this email to your employer/spouse', I would be surprised. Until then, people only have privacy because there's no economic incentive to shatter it. There are no rules. Yet.
Not for this stuff. The EFF has no lobbyists in Washington DC, in fact doesn't even have an office in Washington DC. What they do, they do well: Litigating in court. But don't give them money to influence Congress.
[1] http://www.gunowners.org/114hrat.htm