It's the chorus for Lifehouse's third single "Broken" from their fourth album Who We Are. It was released in 2007.
The chorus is: I'm falling apart/ I'm barely breathing/ With a broken heart/ That's still beating/ In the pain/ There is healing/ In your name/ I find meaning/ So I'm holding on.....
The song lyric that you mention is from the song Broken by Lifehouse. The song lyrics begin with, "The broken clock is a comfort, it lets me sleep at ight. Maybe it can start tomorrow, from stealing all my time."