Power supply for 144 LEDs in parallel?
3V LEDs can't be wired in parallel and plugged into 120V AC socket. 

They will all be destroyed. 

They can only be wired in parallel and powered from (approximately) 3V DC

This article "Hacking a Candleflicker LED" suggest that it might not be practical to wire a few in series either as they appear to modulate their power supply.

Edit:
You could drive them in parallel with a 3-5V power supply.

Assuming each LED is no more than 30mA (0.03A), 33 LEDs would be 1A. A 'wall-wart' would be cheap. (The LEDs might be even less power.)

Edit2:
While we haven't got a datasheet for your tea light LEDs, you might want to compare them to this range of Candle Flicker LEDs to get their current rating.

For example, these Yellow 5 mm Clear Candle Flicker LED are rated at forward current of 30mA. They need a current limiting resistor on each LED. Some have quite significant forward current (abut 3x nominal), so decoupling capacitors would help. Also the power supply should be increased significantly to ensure it has some headroom.

I would build the chain in sections and test them using a multi-meter to measure current, to ensure it stays within the capabilities of a power source. Be careful when measuring current because the LEDs are not on all the time, so the reading might be wrong. Give yourself some headroom.