It depends what you really want when you say, "boost the economy". The reason so many EU economies are trashed right now is because they were fundamentally weak for a long time, ever since the flight of manufacturing to Asia really, and this weakness was covered up through extremely large amounts of borrowing and government deficit spending. In the UK for instance large parts of the north were almost being kept afloat by large deficits run up under Labour. In Spain a lot of employment came from an unsustainable housing bubble that triggered over-construction - construction being an industry loved by politicians because it employs lots of relatively low-skilled labourers.
So these economies were already "boosted" for a long time on what amounts to economic caffeine, and like all caffeine-fuelled energy streaks eventually it comes to an end and the drinker has to crash for a while to catch up on sleep and get things back to normal. People that were being pointlessly employed through bubbles or government jobs programs have to find something more useful to do, which is often really hard and involves complicated retraining, assuming they can even afford that, and then of course such huge amounts of resources were misallocated for so long who even says there are jobs for them to take? In fact there often aren't. This "crashing out on the sofa for 24 hours" is a recession.
Meanwhile tax takes drop, interest payments go up due to the cost of banking bailouts and thus deficit spending rises still further. But that process of adjustment is still required.
The US economy is doing marginally better than most EU economies (except maybe Germany?) because it is still jacked up on caffeine, it never had the crash, specifically, it's jacked up on massive government work programs and the resulting secondary employment, like all the towns that revolve around military contractors working on pointless boondoggle projects. Common sense tells you that the US does not need to sink so many resources into advanced weapons programs or building yet more jets or aircraft carriers. But those people and resources get directed towards such projects anyway, partly because the excuse of national security means it's easy to exclude foreign contractors and get Americans working. American can afford this much longer than most countries can because the dollar is very large, US Treasuries have a privileged place in the worlds financial system, and the Fed has basically broken the US bond markets by buying vast amounts of government debt using newly created money. Theory tells us this should cause inflation. In practice it hasn't become a huge problem yet because the dollar is such a very very deep currency, so it's possible to print more money without impacting the overall supply, and because so many prices are indirectly connected to the price of food and fuel, both of which are very cheap in America.