For a bill to pass, it needs a majority in at least one House subcommittee. Then it needs a majority in at least one House full committee. Then it needs a majority in the entire House of Representatives. In parallel, a bill that is identical in all respects needs a majority in at least one Senate subcommittee, one full Senate committee, and sixty votes on the floor of the United States Senate where objections from even a single Senator can force days of delay. Members of congress need to do all this work while simultaneously fundraising & electioneering, positioning themselves for sundry bids for higher office, etc. The only veto player you need to explain why something doesn’t happen in the federal government is basic human laziness and risk aversion.That's correct, and a very good point. But it's worth point out that many (most? I suspect so, but I'm not aware of a count) bills don't become law by passing through all of those hoops. Many bills that become law the way that, say, the CLASS Act did: by hitching a ride on some other legislative vehicle that was going to pass. Indeed, one of the big stories of the historic 111th Congress (that is, the 2009-2010 Congress) is how many different bills "passed" by getting included in either the stimulus or the health care bill.
What this means is that intense, but small, support for a bill can wind up being enough for it to pass, even if it wouldn't have a majority on its own.
What that also means is that generally intense objections, rather than majority objections, are what's needed to stop a bill. That is, it may appear that bills need to win concurrent majorities in a whole bunch of committees and subcommittees, but in fact many bills never actually get (separate) votes in all those places, so it doesn't really matter whether the bill can command a majority or not. What really matters is whether including something as a provision of a larger bill will spark enough opposition to force a separate vote (or even to place the larger bill in jeopardy).
A bill almost certainly has a better chance of becoming law with a handful of Senators (or well-placed Members of the House) in strong, sustained support against the mostly indifferent opposition of the rest of the whole Congress than it does with very mild, but almost unanimous, approval. Or, of course, than any combination that includes strong dissent (by any Senator or by well-placed Members of the House).
On the whole, I think that leads to reasonable solutions that are properly described as democratic. Regardless of how one assesses it, however, it's important to remember that the textbook "How a Bill Becomes a Law" version of Congress is not, in fact, how things often work.