You can expect  to come on at least 2 discs.

A few days ago, Bioware Senior Designer Manveer Heir stated on his Twitter feed in response to Mass Effect fans that,

The game [Mass Effect 3] is already 2 discs on 360…

“… Fairly sure 360 is 2 discs.”

So expect Mass Effect 3 for 360 to come on multiple discs. This isn’t much of a surprise considering its predecessor was two discs long. For those of you who aren’t looking forward to disc switching multiple times, just think of this way… More discs means more Mass Effect 3 to love.