Hmm. I'd say the biggest argument I could see is that it would result in less stupid bills, e.g. fewer "bridges to nowhere". Maybe less federal bureaucracy. You probably shouldn't really be able to pass something if you can't convince at least 15,001 Americans. On the other hand, logistics would be an insane challenge, and you'd have a huge issue with the inability to have an actual in-person debate. Also, who wants to pay 30,000 people six figures a year? We'd have to stop paying them for it to be practical.

For reference, the current wage is $174,000/yr (a stupidly-high amount). $174,000 * 30,000 = $5,220,000,000. I'm severely disinclined to pay over five billion dollars per year (plus additional logistics costs) for pencil-pushers to sit around deliberating what bureaucratic idiocy they will next hand down from on high.