Andy, Bob & Bill give you good advice. I would only use Mark's suggestion as a last resort and ONLY if you used a 4 flute tap. Taps [and tap extractors] come in 2, 3 & 4 flute models. Each has strengths and weaknesses. The 4 flute model centers in the hole the best, will clear the most chip, BUT is the weakest of the 3 styles and breaks the most easily. The 2 flute tap is the strongest, needs to be reversed more often to clear chips, but more care must be taken when starting it. The 3 flute version is a compromise of the other two. My choice for tapping into tough alloys [4130 of the weldment] would be a 2 flute tap.
An EDM machine will definitely be able to remove the broken tap. That said, unless you live in an urban area, you are unlikely to find a shop which owns one [$$$ piece of equipment]. Using a hammer to drive the broken tap through will surely destroy the threads, requiring re-drilling the hole for a #8 screw [considerably stronger than a #6] It may also leave you with a permanent "rattle", if you can not get the broken tap out of the weldment.
Using a tap extractor is something of an art. I would suggest if you can still remove the weldment, that you take it to a god machinist and have him/her remove the broken tap.
Charlie
PS If you own a "made in China" tap set, run, [do not walk] to your garbage can, and insert said tap set inside.