What biblical/traditional elements lead Catholics to believe that saints can hear our prayers? There have been quite a few questions on the 'orthodoxy' of praying to saints, or rather asking them to pray for us1. Also questions on why Protestants don't/should do the same. My question is slightly more practical: leaving aside whether it's 'allowed' or not: what is the basis for Catholics believing that we might even be heard?

God is omnipresent, so being able to pray to him anywhere and any time 'makes sense'. Even if the saints are currently 'alive' (rather than being in limbo awaiting judgement day), what is the 'mechanism' by which they are supposed to be able to 'hear' our requests?

1 I'm not yet convinced that this distinction is really respected in practice.
Catholic traditions often reach deep into the Jewish roots of the faith and the answer to this question might be best supplied by looking at the Jewish teachings on Caleb who was asked to reconnoiter the land of Canaan and report back to Moses. 

Caleb made a "side trip" to the graves of the Patriarchs (Abraham, Isaac, Jacob) and asked for the heavenly intercession.

As we know, Caleb is the lone voice of optimism for the potential taking of the land.

In the Jewish faith these men and women (such as the Patriarchs and Matriarchs) are called "Righteous" wherein a similar comparison could be made to the men and women of heaven that Catholics call "Saints."