no electrons can not float around as they want! The rutherford model is a classical, non-quantum, model where electrons are orbiting the nuclei as planets orbiting the sun.
But the electrons are then under a radial acceleration, centripetal acceleration, and accelerating charges will emit radiation of continuous spectrum - there will be no stable energy levels and no atom will be stable.
So it means that they are continuously giving radiation of same type in rutherford which give a continuous radiation.
Why the Rutherford atomic model can't explain the line spectra of the hydrogen atom?
In a certain approximation, it can. If your electron starts falling from infinity (or just from very distant place), it radiates a quasi-continuous spectrum. This is called a radiative recombination. But it stops falling into the potential well before reaching the nucleus: its "lowest" orbit is determined with quantum mechanics. In fact, the electron can be captured by the nucleus in some cases (http://en.wikipedia.org/wiki/K-capture). In this sense, it can "reach" the nucleus and form a neutral particle with a proton.