As new supply rises does demand not?
Well, there are two separate things you might be misunderstanding.
Until block 210,000 (around the end of November), about 7,200 BTC are issued each and every day. That doesn't matter if there are two thousand mini rigs operating or twenty thousand, they all are competing for the exact same 7,200 BTC that are issued. Now that 7,200 number can fluctuate a little ,,, if mining goes up 10%, there might be closer to 8.000 but then as soon as difficulty readjusts (in under two weeks at most) the rate goes right back to 7,200 BTC per day.
The second thing you stated was that as new supply rises you suspect demand rises as well. Demand rises at a lower price. So if there is someone wanting to sell aggressively, likely there will be more bitcoins bought at the lower price than would be bought at the higher price. That is standard price elasticity, and demand for bitcoins is elastic based on price.
and publicity could also be taken into account also helping raise the demand..
Ah ..., yes, there could be other reasons the price might go up. You had made it sound like the difficulty going up also meant the exchange rate would go up and many miners get caught up with that misconception.