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The extreme pressure and temperature greatly reduces our ability to drill holes deeper than some kilometers into Earth's mantle.
However, on a body smaller, colder and less dense, this would be a significantly easier task.
Could a human-supporting tunnel be built into the centre of Enceladus (Saturn's satellite) using near future tech (mainly present day materials)?
No. First of all, you hit ocean under the ice, so you need a sealed tunnel there, not a hole.
Although smaller than Earth, it is still warm enough to melt the magma, so you need a tunnel capable of keeping out thousand-degree melted rock.
Meanwhile, the ice and the mantle are in motion. Any tunnel lining needs to hold back an enormous momentum. Ever consider stopping a glacier? This is orders of magnitude worse.
To reach the center, you need 250 km of tunnel, which doesn’t sound that bad. But it is through layers that move and have (still) enormous pressure and temperature beyond any near-future material’s ability.
