BioWare has stated previously that you can gain "effective military strength" through any combination of single player or multiplayer. Single player play contributes "War Assets" while multiplayer contributes "Readiness Rating." These two things multiplied together are a big factor in your ending.
[...] SP can still be played all by itself without any kind of multiplayer or third party and you can still get the absolute best ending. [Multiplayer] just gives you new options to be able to get that ending.
Also in a different interview with Penny Arcade:
You can get best possible outcome in the game by just playing single player if you want, as long as you are willing to do a lot of the side missions and content. However, maybe you only want to do a critical path run of the single player. Well, by playing multiplayer you also increase your galactic readiness rating can affect the final outcome. Using the iPhone Datapad app and the iPad Infiltrator game will also tie into Galaxy at War and update this final rating.
However, it might be challenging to just play the single player. From this PC gamer review:
The game’s still story-driven, and it doesn’t end until you’ve completed the main series of missions. But when you do, what happens in the final cut-scene depends on how many War Assets you have accumulated.
It is possible to get the best ending in single player without playing multiplayer, but it’s twice as hard. All your War Assets only count for 50% of their potential value.
Their intent is to allow people to rush through the single player campaign (if they don't care for the story or side missions) and play a bunch of the multiplayer, and still get the "best ending."
Now that I've finished the game, there's a couple of things I'm going to add to what BioWare has said. While BioWare claims that you can get the "best ending" without playing multiplayer (or the tie-in titles for other platforms), I find this statement to be misleading at best.
It's incredibly unlikely that you will be able to get enough war assets for the "highest tier" endings to Mass Effect 3 without anything increasing your Readiness Rating. You'd have to have played ME1 and ME2 pretty thoroughly, making all the "correct" decisions in your save to import into ME3. Alternatively, you'd have to start from a "perfect" ME2 save import in order to get anywhere close to the number of War Assets you'd need. If you're not importing a previous save, your chances at playing only the single player and seeing the "best" ending are abysmal.
Additionally, you'd have to play this game through very carefully, making sure to maximize your War Assets. Most decisions in the game effect your war assets, and if you don't know ahead of time what the "best" decisions are, you're likely to end the game with significantly fewer assets than you need for some of the "best" endings.
I played fairly well through both previous games, skipped the DLC, and got nearly every war asset possible in ME3. I still fell a good 20-25% short on War Assets required for the "highest tier" ending.
Having said this, the endings are extremely similar. Regardless of how you play, you're highly likely to have very similar options in your ending choices, and each of the endings plays out extraordinarily similarly.