At this point in time it seems doubtful that we could intercept and deflect an asteroid large enough to justify being deflected. This is simply a matter of momentum, a large asteroid has a great deal of momentum and the puny little spaceships we can presently intercept an asteroid with can impart only very little momentum. The only way we can substantially alter this formula is by using nuclear weapons.
The wikipedia article states:
If the object is very large but is still a loosely held together
rubble pile, a solution is to detonate a series of nuclear explosive
devices alongside the asteroid, far enough away as not to fracture the
potentially loosely held together object. Providing this stand-off
strategy was done far enough in advance, the force from any number of
nuclear blasts would be enough to alter the object's trajectory to
avoid an impact. By the 2020s NASA has concluded that 1 mission
utilizing nuclear stand off, can deflect NEOs of 100–500-metre
(330–1,640 ft) diameters two years before the estimated Earth impact,
and larger NEOs with a five year warning.
A NASA analysis of deflection alternatives, conducted in 2007,
Nuclear standoff explosions are assessed to be 10-100 times more effective than the non-nuclear alternatives analyzed in this study.
Other techniques involving the surface or subsurface use of nuclear
explosives may be more efficient, but they run an increased risk of
fracturing the target NEO. They also carry higher development and
Nuclear standoff (detonating a nuclear warhead near the asteroid) would seem to be feasible, but would require at least 2 years warning.
There is one way to deal with an incoming asteroid, not actually precluded by the question, that we definitely have the technology for - evacuate the area and let it hit us. These asteroids, while destructive, are not that destructive. The Tunguska event, for all it's boom, was only like a large nuclear bomb. Humans have detonated larger nuclear bombs on the surface of Earth, most famously the Castle Bravo nuclear test, and the Tzar Bomb. We can survive being hit by an asteroid. Most of Earth's surface is sparsely or unpopulated and an asteroid impact would carry little danger to humans.
Even much, much larger asteroid impacts leave no evidence in the fossil record of species extinction. For example the Manson Crater in USA:
Most researchers agree that the 35-km-diameter Manson Crater of Iowa, a possible source of shocked quartz in the K-T boundary sections, was too small and insignificant to have caused mass extinctions.
The impactor in that case is thought to have been a 2km diameter stony meteorite, much larger than the Tunguska event impactor, and it is still small and insignificant when it comes to causing extinction. Now this is not to say that such a large impact would not be incredibly disruptive, but it would certainly be survivable, it is not like there is an imperative to avoid it.
This makes evacuation a legitimate strategy, the impact is only going to be extremely lethal at ground zero, or where it raises tsunamis if it lands in the ocean.
With forewarning - even only weeks or days - there would be time to relocate people who would be at ground zero. Those areas which would be at risk from secondary effects such as ejecta, tsunamis, earthquakes and volcanic eruption could also be evacuated, or at least emergency services could be on heightened alert.
Note that if the asteroid is broken up rather than deflected while still somewhat distant from Earth, it would cause much, much more damage. This is the MIRV warhead principle, a lot of smaller explosions spread over a large area causes much more damage than one large explosion. Thus intercept is not without risk and it might be safer to take the hit than to risk breaking up a 'rubble pile' asteroid with a nuclear explosion. Nevertheless, if the asteroid is aimed for a major city, a mission to deflect it might well be cheaper than the costs of dealing with a natural disaster of that magnitude. For example cleanup/reconstruction costs for large earthquakes which level a major city measure in 10's of billions, while space missions are often only in the 100's of millions or a few billion. In the event of a major impactor, it would come down to a cost analysis like this, how much would it cost to deflect it, versus the costs of dealing with the damage an impact would cause?
In sum, early detection may well be the best form of preparation we have, as it gives time for orderly evacuation of the danger zone, and the relevant emergency services can be ready to respond.