Unfortunately, United States has a population of ~330 million and that would mean a House of Representatives with 33,000 members. There's no way it would be able to effectively deliberate topics with that many people. Just imagine how little time each representative could be allocated to speak, given there are only 8,760 hours in a year. Additionally the individual power of each representative would be so watered down as to be practically meaningless.
It's an unacceptable solution but it seems to me that the US is just too big and splitting it up would make more sense.
Why do people need to debate on the house floor? Do such debates actually change anyone's mind or how they vote? Let them debate in an electronic forum with written arguments, let them debate in public and on social media (a good portion of political debate already happens on social media). Debate on the floor isn't so sacred we can't do without it.
And yes, the power of individual representatives would be watered down, that's ok. It would be much closer to the direct democracy the parent comment suggested (and the reason I brought it up).
It allows representatives to deal with boring bills the public doesn't care about, but there are enough representatives that I can reasonably expect to be on a first name basis with my representative if I care enough to get involved.
Debate on the floor of the House and Senate is largely faked for TV cameras already in the current era.
CSPAN camera angles are limited on purpose to hide this, but most speeches are given to an empty or nearly empty chamber. Actual floor debate that might change viewpoints is rare to non-existent now - the real debate and discussion happens off of the floor in private intra-party meetings and lunches, or in 1:1 meetings between leadership.
