Geopolitics and distrust among Allies
When we look at geopolitical situation in Europe between world wars, we could roughly divide all countries into three groups. First would be so called conservative group, ranging from parliamentary democracies to monarchies that wanted to keep status quo. Typical representatives of this group would be Britain and France, but also smaller countries like Romania and Yugoslavia. These countries wanted to keep present borders and power balance. Second group would be international socialists (Marxists) . This group would include just one (huge) country - USSR, but it would include various leftists political movements all across the continent and in broader sense the world. Of course, goal of this second group was revolution and possible change of borders. Third group would include counties of so called Third Position (sometimes called Third Way) . Representatives of course include National Socialist Germany, Fascist Italy and other smaller satellite countries of these two. Ideologically opposed to international socialists but also wanting redesign of borders and some kind of revolution. Simplifying things , politics in Europe was power play between these three, and for each side there was a danger of other two ganging up on them, creating dreaded two-front war. This was a major concern, and influenced lots of moves before and during WW2.
What were Stalin's geopolitical goals ? We could judge about that because he mostly managed to fulfill them. He was not so much into recreating borders of Russian Empire before WW1. From Poland, he mostly wanted lands east of Curzon Line, which he felt were ethnically Ukrainian and Belarusian and taken because of the weakness of USSR in Polish-Soviet war 1919-1920. Similar position with the Finland, and Baltic states were incorporated as republics into USSR. But, he did want to spread socialism (communism) as far as possible into the world, and all these socialist countries would be under guidance of USSR and him .
Anyway, USSR begun physically clashing with Germany and Italy already during Spanish civil war 1936-1939. But, "conservative" group of countries (Britain and France in particular) mostly kept neutral in this conflict. This lead Soviets (i.e. Stalin) to believe that "capitalists" want to let USSR and Germany bleed themselves dry, and then simply pick up the pieces. This idea, as we could see later, became ruling principle and guiding leitmotif of whole Soviet diplomacy during the era. It was reinforced when during Sudeten crisis Britain and Poland refused to face Germany militarily (although Soviet Union wanted to do that) thus letting Germans take what they wanted.
Soviet response was Molotov–Ribbentrop Pact which subsequently allowed USSR to be in position of watching others battling it out (and losing men and resources) . Stalin's blunder of not believing in German attack in 1941 was partially made because he believed that Britain (being in bad position at the time) would do anything to pit Germany and USSR against each other. And when the war actually started and after the war, Soviet position was that Allies (mostly Britain, US not so much) purposefully delayed Second Front in order to weaken USSR and conserve their own strength. After the war, Soviet propaganda carried this idea even further, claiming that British secretly cooperated with Germany. Typical representative of this idea was movie The Fall of Berlin, which was made was Stalin was still alive in 1949-50.
It should be noted that there were some half-attempts of Soviet-German peace talks during the war, although all of this remains under veil of secrecy even today. For example, it is known that immediately after the start of war Soviet diplomats sought contact with German diplomats in Sophia, Bulgaria which was pro-Axis but didn't declare war on USSR. Perhaps biggest chance for separate peace was during spring rasputitsa in 1943, usual lull in fighting on Eastern front and both sides being exhausted (German loss at Stalingrad and subsequent Soviet loss at Third Battle of Kharkov) . In any case, West was partially aware and even more afraid of this possibility. Therefore, they certainly could not delay Second Front much more than summer of 1944.
What was Soviet position in first half of 1944 ? Despite huge advances in 1943 and winter of 1943/44, front lines were still in Soviet territory. Belarus still had to be liberated, also western parts of Ukraine and Baltic republics which Soviets considered as their own. Soviets did plan Bagration, Lvov–Sandomierz and other smaller offensives, but each German division that was sent to France was division that Soviets would not need to fight. Consequently, instead of Soviets being bleed dry, now Allies would have to shed their own blood fighting Germans. Theoretically, with D-day being postponed (again) Soviets would have no choice but to launch those offensives regardless. However, Germans would likely reinforce the front with some divisions from France (at they did in winter of 1943/44, despite divisions like Leibstandarte SS Adolf Hitler being earmarked to be armored reserve in France). Therefore, Soviet advance would be costlier and likely less successful in terms of territory being gained.
Overall, biggest Soviet (and especially Stalin's , do to his paranoid nature) fear was of Pyrrhic victory over Germany, only to have US and UK walking in, possibly even attacking USSR (similar to Patton's designs ) . Historically, Soviet Union had much larger causalities than Britain or US, and much larger level of devastation, which is felt even today. There were catastrophes even after the war like famine of 1946-47, caused by huge casualties in working population. Without Second Front, this would be even higher, so not only Stalin would not have an empire stretching to France, he would likely had difficulties keeping USSR as functional state in pre-war borders.