First Manassas was in July, 1861, which gives
what if the North had won the first battle of bull run in the american civil war? how would things go? would the civil war be shorter?
First Manassas was in July, 1861, which gives the US a solid four months of campaigning to follow; if the victory results from McDowell gettting his entire 35,000 men into action (historically, only about 18,000 actually moved south of Bull Run, which puts the "rebel victory" trope into perspective), the realities of mid-Nineteenth Century infantry tactics (as demonstrated by the British on battlefields stretching from the Redan to Rangiriri to Ridgeway, or the rebels at Liberty and Hoover's gaps) are that casualties will be high, whether on the offensive or defensive...
So McDowell's forces will have to reorganize and be reinforced, although the US does have Mansfield's garrison force in Washington (~6,000) and Patterson's force in the Shenandoah (~11,000), and the closest source for the rebels are their forces around Richmond and southeastern Virginia, who have to keep an eye on the US forces at Fortress Monroe and Hampton Roads; likewise, this comes after Lincoln's May call for an additional 11,000 regulars and 42,000 3-year-volunteers, and coincides with Congresses' approval of 500,000 3-year-volunteers (note this coincides roughly with the number of long arms in the US arsenals, not with troops, in April, 1861), so the contention the US was somehow unwilling to make use of their demographic and industrial and economic advantages over the rebels is incorrect.
As Anaxgoras points out, their are multiple solid defensive lines between Centerville and Richmond, of course; and given JE Johnston's historical decision to evacuate the Centerville position in 1862 when McClellan even threatened an advance, it's a safe bet the rebels will be withdrawing south after a lost 1st Manassas and may not stop short of the Rappahanock or Rapidan.
An Overland Campaign analogue in 1861 is challenging for the US, largely because of the issues inherent in a mobilization, but the US forces - even under McDowell - are presumably capable of grinding forward, river line by river line, before winter sets in...
It's an interesting point of departure in terms of command, of course; this predates Lee's ascension (he's assigned to Western Virginia), so he's not even in the mix - although depending on which of the rebel commanders is seen as responsible for the defeat (Johnston or Beauregard) it's possible Lee may be called in (since this also predates his defeat at Cheat Mountain); another possibility is AS Johnston, although he'd barely made it to rebel territory in Texas by the summer of 1861.
The US divisional commanders under McDowell and Patterson in this period include Tyler, Hunter, AJ Porter, Heintzelman, Runyon, Miles, Cadwalader, Dix, Keim, Sanford, and Mansfield, among others. McClellan is in West Virginia but has yet to win much of anything...
Interesting point of departure, and certainly more plausible than most dealing with the Civil War in 1861.
Best,