Well, he tried the starving off Britain, and was at it at full power even as soon as in the BoB.
Indeed.
The infamous "Directive No.21. Operation Barbarossa" issued by Hitler himself, clearly states;
The Air Force will have to make available for the support of the Army in the Eastern Campaign forces of adequate strength to ensure a rapid termination of land action and to give the East German territories maximum protection against enemy air raids. This making of the main effort in the east must not be carried to a point at which we can no longer adequately protect the totality of our battle and our armament zones against enemy air attacks, nor must the offensive against England, and in particular against England's supply routes, suffer in consequence.
This, coupled with Tilt's earlier comments:
Hitler thought the whole thing a distraction from his Eastern European ambitions and eventually just wanted London bombed into submission.
... brings out an interesting question as to what the real intention behind Barbarossa were.
Hitler's Directive No.21 is quiet clear, and strategically sound, in pointing out certain conditions were to be met to achieve total victory over the Soviets. Amazingly, despite the historical success of the German military 'blitz' for a whole year after Barbarossa started in June of 1941, it turns out that none of the major obectives and conditions Hitler set with Directive 21 were ever actually met.
The Northern armygroup failed to take Leningrad (Leningrad survived for the entirety of the war), and consequentially the Center armygroup failed to cooperate with the Northern group in driving to Moscow. The very warnings and dangers the Directive has cautioned about the Luftwaffe in the Eastern Front, were realized during 1942. The prime objective of Barbarossa, which was to form a Volga-Archangel line, to sever the Soviets from their important industrial provinces, were ultimately foiled, due to the Soviets' amazing evacuation of industry to Siberia.
But the most important of all, the very beginning of Directive 21 states;
The armed forces of Germany must be prepared, even before the conclusion of the war with England, to defeat Soviet Russia in one rapid campaign ('Operation Barbarossa').
This more or less implies that Hitler clearly thought the war against England would take a lot longer than even one against USSR. Hitler's ambitions in the Eastern Front was certainly big, but still, he seems to have thought that the Eastern Front campaign would as swiftly end as the offensive of Ardennes.
The Eastern Front offensive, particularly the intended final destination of the Southern armygroup - the Caucasus, Grozny, and Baku, all rich in oil - seems to imply that Hitler was preparing a very-long standoff against the UK, in which oil reserves would become critically important in case 'unreliable' Stalin would become uncooperative in exporting fuel sources.
This is made clear in that the final parts of Directive 21 mentions;
It is important that all Commanders-in-Chiefs make it plain that the taking of necessary measures in connection with this directive is being done as a precaution against the possibility of the Russians adopting an attitude towards us other than what it has been up to now.
Hitler viewed Stalin as an 'unreliable', and possibly 'potentially hostile' ally.
So it would seem that Hitler decided Operation Seeloewe would never be realized without some kind of long-term preparation, and decided to claim major Soviet provinces with high industrial capacity and oil reserves, before Stalin ever got the chance to become hostile towards the Third Reich.
It was basically a "pre-emptive strike" of WW2, intended to end quickly, with rich rewards. At least, initially it seems Hitler viewed the Eastern Front as lasting shorter than the Front against England - until the Soviets refused to cave in, and things started to get out of hand.
note) The word 'pre-emptive strike' used above is not in conjunction as the same wording 'pre-emptive strike' used by, for instance, Viktor Suvorov, who views Barbarossa was a 'pre-emptive' strike against a realized Soviet threat against Germany, in which he views the mobilization of the Soviet armies in the border regions as being offensive, rather than defensive, in nature. The 'pre-emptive strike' as I have mentioned, is more of a psychological one, in which Hitler either misinterpreted the 'Soviet threat', or through paranoia, decided to attack first in case the USSR would become hostile.
The 'pre-emptive strike against realized miliatry threat' theory, as that of Suvorov and those who share his views, are largely discredited nowadays.