How do I hook up an LED across the tx pin on my Atmega328?
In general it is not a good idea to draw a lot of current from your Rx and Tx lines to drive LEDs. The extra current draw can reduce your Fan-out to your target.

To avoid extra current draw from your lines, you can use a dual OpAmp like LM358D to drive those LEDs.





The high impedance of the OpAmp inputs will not draw much current from your Tx and Rx lines and will preserve the fan-out on the lines.

I have simulated this schematic in LTSPICE and physically verified with LM324 (TI) on a breadboard. Sorry did not have a LM358D handy but they work similarly. 

Edit:
Thanks to pointers by arudino.tyro. I was able to try out the new schematic with LM358D. Old schematic is here: http://i.stack.imgur.com/GHauy.png