This goes in the category of things you probably shouldn’t adapt from the Obama campaign for your organization.
The Obama campaign tested most everything. As Alter describes, they  even (wisely) ran tests against their experience and hunches. As the campaign progressed the need to raise more (and more) money became more (and more) pressing. Good sense and experience told the email team that too much email would annoy people to the point of tuning out, unsubscribing or maybe just not voting.
You know what’s smart? Testing the frequency of your emails.
Being annoying (after extensive testing) was worth $100 million
“For a while, yellow backgrounds generated 10 to 20 percent more email responses than white backgrounds. Who knew? The fundraising emails – more than four hundred in all – appeared hour after hour, day after day because they worked. An elaborate ‘More Emails Test’ showed conclusively that the more fundraising emails that went out, the more money came back – simple as that. Even the $3 ask – just enough to cover the credit card processing – helped build lists and increase a sense of ownership on the part of supporters. The growth in the number of people unsubscribing because they couldn’t stand the alarmist emails was much slower than the growth of cash flowing in, and Chicago knew that peeved unsubscribers would end up voting for Obama even if they thought the emails sounded like sketchy pleas from Internet con artists. Goff concluded that ignoring the human desire not to be annoying may have been the single greatest conceptual breakthrough of the campaign. It turned out to be worth more than $100 million.
Don’t do what those guys did (unless you test it first)
Their tests found that being a pain in the ass worked in their favor. I’d say test this yourself (it could work) but the Obama campaign didn’t care what subscribers thought as long as they donated and voted. Your organization, however, needs to build lasting relationships to raise money, win drawn out policy fights, and build movements.
If you test it and really pay attention to the data you’ll find that more email is sometimes better. Sometimes not. Don’t rely on hunches and your (or a consultant’s) experience based on work with other groups or campaigns.
Either way, it’s worth remembering that you’re (usually) in it for the long haul. Like trees with deep roots, strong relationships bear fruit for many years. Be interesting, results-driven, and valuable to your supporters. Not annoying.