households dont have tax in them, thats the main one
so the government should get back alot of the cash quickly back via tax on the payroll taxes and vat.
so say hs2 builders get 100billion, the government gets (random figure im making up) say 30% back on paye and vat purchaces of the builders. but they also get a % of whoever is down the line, so say they all the workers by stuff from the market, and furniture etc, the government gets a % of each transaction, one way or another. its a cycle of money.
while a household you might spend out say a grand on doing the garden, and while you now have a nice garden and higher property value, your not getting any of 1k back in taxes, and per household your benifit from stimulating the market/economy is very small.
and that does have an effect on how you set out spending on things, either trying to maximise "churn" of money, or reduce expenditure, slowing the chern/economy, but saving money on the starting outlay.
both are gross simplfications and not 100% correct ofcourse.
but if household budgets and government budgets where the same, the 2010 tories could have easily worked out how much needed trimming the balance the books, the deficit was quite low % wise this souce puts it at 1% before the recession

. trimming 1-1.5% off government spending seems not too hard, much different from the level of cuts we have had.
https://www.ukpublicspending.co.uk/uk_national_deficit_analysis