Image if Singularity's effect does not say "Deal 6 to each of up to two units.". Instead it says "Deal 6 to two units.". If there are only 2 enemy units with Deflect 1 on the board, and if I refuse to pay the 2 additional power costs for the deflect on the 2 units, does this spell still go onto the chain?

No. With mandatory wording ("Deal 6 to two units"), the spell requires two targets, and those are the only legal targets — Deflect 1 on each makes the two Deflect payments mandatory additional costs. If you refuse to pay them, the spell cannot be played and never goes on the chain.

Deflect isn't optional: it reads as "spells and abilities an opponent controls that choose me cost [X] more Power to play as an additional cost for each time they choose me" (Rule 809.1.c–d). Because the hypothetical requires exactly two units (no "up to"), you can't dodge it by targeting zero or one — so the total cost includes both Deflect surcharges. If you choose not to pay during the Pay Costs step, the act of playing the card is undone and the play is cancelled (CR 445.2.a, 358.5); the spell never becomes a Finalized Chain Item.

Contrast with the real Singularity, which says "up to two units" — there you may simply choose fewer targets (including zero) and avoid the Deflect costs entirely.