120 outlet jump from a dedicated 240 dryer line
 

Is it possible to intercept a 3 wire (romex) dedicated line to my dryer and splice in a 120 receptical off one of the two hot leads in the romex line?

run out and get what's called a sub panel. Hook it in to the line. You'll now have two 120 lines that have their own breakers.

low on funds and in a hurry if im verry careful and thorough can this be done?

I would tend not to recommend it, because your 220 line is using a common neutral wire, which means you'll have a non-connected hotwire sitting out there waiting for an excuse to close a circuit.

Now what you CAN do, if you don't need to use it as a dryer outlet anymore, is remove the 220 breaker that feeds that line, and replace it with a single pole. That will kill the second hot wire and turn the romex into a 110 line with an extra wire that's not connected on either end. Of course, you'll need to put a standard outlet in there (assuming you want an outlet) but they're cheap. The breaker shouldn't cost you more than $10, and that's assuming you have something relatively expensive like a SquareD QO or something.

Sorry I haven't explained my situation well. I need a 120 receptical in a location that has no wireing around except my dryer line which is the 3 wire dedicated line from the panel. I still use the dryer and the line I just want to splice in a jumper to a receptical using one of the hot legs in the line. I was just unsure if doing this would cause complications with the dryer or the line itself. By the way, thanks. I appreciate your time and input.

ahhhh, i getcha now. No, you should absolutely not do that - you're setting up a very dangerous situation if you do. Your best bet is to either wire it right, which is a ROYAL pain in the ass, or just run an extention cord.

Listen to those who tell you not to do it, it's potentially very dangerous and also illegal according to the NEC. Wire it right (or use an extension cord) and save someones life down the road because the life you save could be your own.