If McClellan manages to break out anyway, then it's basically historical. If he doesn't manage to break out, and the Army of the Potomac surrenders as a result of being cut off from supply, then the Union is in serious trouble.
As of 30th June, when Pope was newly in charge of the Army of Virginia, it numbered about 68,000 PFD; this basically entailed stripping the defences of Washington (which were down to 3,800 PFD) though the Middle Department (defences of Baltimore, Harpers Ferry garrison and generally covering the north shore of the Potomac) was about 15,200. In addition to this historically about 14,000-15,000 men were pulled from Burnside and Hunter's departments to go to McClellan (and would later become 9th Corps) though these wouldn't arrive straight off owing to travel and organization time.
So the highest you can get the size of the field force able to oppose Lee is about 83,000 PFD once "9th Corps" finishes arriving in late July, and it has the disadvantage of being commanded by John Pope.
By the same measure, the Confederate army that fought in the historical Seven Days was about 112,000 PFD (this number may actually be a low estimate, as startling as it seems) and here with the extra couple of brigades' worth of troops to form the blocking division that can be estimated as about 120,000-125,000 disposable troops after the Seven Days but without taking casualties into account.
The historical Seven Days involved 20,000 Confederate casualties, of which 9,800 took place in the post-Gaines-Mill sequence; this basically means Lee has a bit more than 110,000 PFD available. He can quite feasibly invade Northern Virginia with a hundred thousand men PFD, a larger force than Pope has (historically Pope got reinforced by two corps of the Army of the Potomac and was opposed by more like 50,000 men PFD than 100,000 men PFD, and still lost badly).
Given the historical timeline of reinforcements arriving for the Union, new regiments won't start to come online until late August to September, which means that any battle in July or early-mid August is one in which Lee can confidently claim the numerical advantage (after which point very green regiments start to reinforce the Union, which redresses the numerical balance but perhaps not the combat power one); it's not really feasible that Pope can avoid engagement for a month like that without retreating into the Washington Defences, and if he does then Lee can manoeuvre against Baltimore or go north into Pennsylvania... or place Washington under close siege, if he happened to capture the AotP siege train with the army.
To summarize, it means the Union's boned.*
* this does not mean they can't win; it means they need to outperform to get through the next few months.