Well, let's peek at the world of voting paradoxes, though I'm not sure this is even a paradox. Weirdness, maybe.
Imagine a population:
40% responsible liberals, who want high services and taxes to pay for it ("Massachusetts")
40% responsible conservatives, who want low taxes and will take low services ("New Hampshire")
20% who either irrationally don't think things through, or rationally but selfishly figure they can move to another state after the system collapses, and either way will vote for low taxes and high spending. (no stereotype)
Now imagine a ballot with both a tax cut and a spending increase on it. The former will get 60%, from the conservatives and the others, and the latter will get 60%, from the liberals and the others. Voila: irrational (well, budget busting) results, despite only 20% of the population being irrational or uncaring.
And it doesn't have to be even or as much as 20%. 45-35-20, 45-45-10, 49-49-2, 49-41-10. Lower margins but same outcomes. 98% could be making responsible decisions but the vote doesn't come out that way.
Before dumping on "direct democracy" as a concept, let's look at the real problems. Most obvious is voting on the measures in parallel, without any idea of how the other one would come out. If voting were sequential, truly responsible voters could deal with that -- tax cut wins, liberals regretfully vote down services, or vice versa. Of course, in this case the outcome becomes very order-dependent, power accrues to whoever can set the sequence. And sequential voting doesn't work well with existing balloting practices and frequency.
Another fix is to identify contradictory laws, and force voters who vote for both to also make a tiebreaker vote; Switzerland does this, IIRC, not that Switzerland has voters proposing laws or spending. (Initiatives are for constitutional change, and the legislature is responsive enough that there's no need to go to the voters for budgets -- unlike Cal where you can avoid the 2/3 barrier in the legislature.) That calls for someone making such decisions. With high feedback that could be done democratically: vote on the consistency pairs of ballot proposals, though combinatorial explosion happens quickly.
Yet another is requiring spending measures to include their own tax raises; Oregon does this, though it doesn't solve the general problem of inconsistent laws. Would also prevent a democratic force-through of a Keynesian stimulus, should such ever be needed.