Hamilton and Madison however both also believed government should be as big as it can be, and democracy with it (which may have been an early stab at arguing for universal suffrage). Madison wrote in the federalist papers that making democracy and government as big as possible was a crucial vanguard against corruption (the exact opposite of what libertarians think) - because big organisations get filled with competing interests, and the more competing interests there is the harder corruption becomes - there is always somebody who will personally benefit or be able to advance the interests of his group by ratting you out.
The US government - even at it's barebones just-the-congress-and-white-house is already one of the largest on earth, and that's how it was STARTED. Two houses of congress, each with hundreds of members - the average parliament has half as many members as the house of representatives, and even in countries with two (common) that's still typically half the number of lawmakers. You appoint several representatives per state - two senators for example, while most countries get one representative per represented area (which, granted, is usually smaller regions - typically covering a city or such). Then there is the state governments below that, which are significantly larger and more powerful than the average provincial government - and the metro-level governments below that: ditto.
Same with welfare - having a welfare system has been part of the US since it's foundation - indeed it was one of the requirements for statehood, before a territory could become a state it would have to have a welfare system implemented. Andrew Jackson refused to sign Brigham Young's appeal to grant statehood to Utah until Utah had a welfare system that extended beyond the membership of the mormon church (and was not run by said church).
And frankly - they were right. The most corrupt governments in the world - are also the smallest and provide the least services, with the least number of government employees. The most corrupt government of all is the dictatorship - which ultimately shrinks the all the powers of government into a single person. The most successful nations on earth, with the highest standards of living and the lowest levels of corruption are also the nations where the governments are the largest, the markets the most heavily regulated and the government-services cover essential public needs the widest.
In a small government like in the D.R.C. you can get a sitting president refusing to step down as he approaches a term limit - and the government unable to budge him leading to violent clashes in the streets as the citizens try to do the government's job for them (and come up against the loyalist parts of that government and it's military apparatus - so much for the gun-nuts assertion that in a revolution the soldiers would side with the people, the world is full of revolutions and that NEVER happens) - clashes which have killed tens of thousands in the last few months.
Now imagine if Obama tried to pull that stunt? Not that he is likely to - I think he can't wait to get the fuck out of that house - but just imagine if he did. The republicans would be in uproar and they would remove him from the white house, by force, if needed - and they military would not obey him because there are enough republicans in the senior command of the pentagon. It would take seriously weird circumstances to even get to a civil war, in reality no president would try because the odds of success is just too low - the government organs set up to provide oversight over him are just too large and powerful to try and resist.
That is whats good about a big government - but one constrained by a constitution that strictly limits what they may apply their sides and power to. Competing interests - so that if anybody tries to abuse their position too much, there will be somebody else who can score big by busting their ass.
Of course, what Madison could not have predicted was a world where a wealthy elite could buy nearly all the politicians on BOTH sides... and turn their competition into loud but meaningless squables that are never about anything substantive. The working parts of the plan is the competing interests of entire branches of government with each other, but there is no more competition WITHIN the branches - that's a bad thing, and why the next ammendment really ought to make election campaigns publicly financed and outright prohibit all donations. Just take the money out of politics. Sure it is censorship - but this is actually one of those rare cases where that's a good thing, because what you're censoring is corruption. It isn't a contribution to the democratic process - it's an undermining there-off.