I DO= The verb DO can be a pro-verb (a pronoun replaces a noun, a pro-verb replaces a verb). A pro-verb substitutes for a verb and its complements, so in this sentence, I DO means "I imagine me and you", as it was said in the previous sentence.

HOLD= Embrace, hug, put your arms around somebody.

IF I SHOULD CALL YOU UP= We can use the modal verb SHOULD (or MIGHT) in an if-clause to express the idea that it is not very probable.

CALL YOU UP= Phone you. We can also say "ring you up".

INVEST A DIME= Spend a dime. To invest is to spend money but then you will get a benefit from it (in this case, an emotional benefit if you accept me)
DIME= An American coin which is worth 10 cents (it comes from the French word "decime", tenth)

TO EASE= To calm, to relax, to stop from worries.

I CAN'T SEE ME= I can't imagine myself (doing that).

TOSS THE DICE= DICE is the plural of DIE, wich is a square cube with dots on each side going from 1 to 6. To throw the die, or to toss/cast the die is to throw it rolling to see what number you get. It is used for gambling (a game where you bet money)

IT HAD TO BE= Also "it was meant to be" = it was our fate (change it), nothing could change that future event.