According to Wikipedia, you will need an Origin account for both the single-player and the multiplayer campaigns in ME3.
Customers purchasing PC editions of the game (retail or digital) will
be required to install Electronic Arts' content delivery and digital
rights management system, Origin. The Origin client (and an Origin
account) is required to install, activate and run Mass Effect 3 on a
PC for single and multi-player portions of the game.
This Bioware forum post by Chris Priestly gives a lot more detail around Origin and Mass Effect. Specifically, it speaks to your question:
Is constant Origin connection required or is it a single one off
authentication when the game is first installed. Is there also a limit
to the number of installations available? Mass Effect 3 will require a
one time, single authorization for the single player game. There is no
limit to the number of installs. Playing Mass Effect 3 Multiplayer
will require a constant connection.