Not at all. The public would not be willing to surrender just because Washington DC fell.
The U. S. Capitol has faced violent incidents several times in its history. Key events include the Burning of Washington in 1814 and the January 6, 2021 attack.
1. The Burning of Washington (August 24, 1814): British forces captured Washington, D. C. during the War of 1812, setting fire to the Presidential Mansion and the Capitol, marking the first time a foreign power occupied the U. S. capital.
2. The January 6 attack: Supporters of President Trump stormed the Capitol to overturn the 2020 election results, disrupting the certification process and showing the risks of political violence in America.
Also, before Washington, D.C. became the permanent US capital, eight different cities served as temporary capitals. These cities were: Philadelphia, New York City, York, Pennsylvania, Lancaster, Pennsylvania, Princeton, New Jersey, Trenton, New Jersey, and Annapolis, Maryland. Capital Hill, specifically at the summit of what was then called Jenkin's Hill in Washing, D.C. The cornerstone was laid in a public ceremony by President George Washington on September 18, 1793.
Washington D.C. is America's capital and it is nostalgic. I would be very pissed off if it were attacked or destroyed, but it can move wherever it needs to be, and Americas will still FIGHT LIKE HELL to defend the rest of the country. The American spirit and national identity are not defined by a single building.