It is possible though cost&complexity seems high - we theoretically can even today bundle a bunch of SR-71 engines and probably stretch them beyond designed Mach 3.3 for the short time. Having low thrust-to-weight (SABRE promises up to 14, SR-71 had 6) we'd need either a lot of them for VTOL which leads to high cost, or we're limited by the size of maximum realistically possible hypersonic capable plane, plus the plane body being the additional weight. For example VTOL calculation - say engine weights 1 ton, we can lift off 13 ton of fuel and payload. It will use 40 ton of O2 from the air. For rocket engine - 1 ton engine can lift off 100+ ton, and if we just take the 13 ton fuel plus 40 ton O2 we'd have 45 ton budget for the rest (body plus payload). In reality you'd need higher fuel ratio, and this is why VTOL for atmospheric breathing engine pretty much isn't an option .

Going beyond pure rocket engine for the 1st stage i think air-augmented rocket (http://astronautix.com/g/gnom.html) being simpler (thus cheaper) would be the next step that would get us closer (specific impulse wise) to what SABRE is targeting.