Does burning the White House count?

From post-Revolutionary War to the War of 1812, many of the Founding Fathers felt that they would be able to defend the country solely or primarily with militia. There was massive fear that a standing army was the country's greatest threat.

“A standing military force, with an overgrown Executive will not long be safe companions to liberty. The means of defense against foreign danger, have been always the instruments of tyranny at home. Among the Romans it was a standing maxim to excite a war, whenever a revolt was apprehended. Throughout all Europe, the armies kept up under the pretext of defending, have enslaved the people.” - James Madison to the Constitutional Convention, 1787

Britain's ability to burn parts of Washington, DC, and nearly take New Orleans while primarily focusing on Napoleonic France showed that Britain was still a credible threat, especially being able to operate from Canada.

Given that France had a formidable army and navy as well, they also should be considered to have been a credible threat, given their access to Caribbean bases and later access to and then ownership of what was then Louisiana prior to the Louisiana Purchase, had they not been constantly at war with all of Europe.

The third obvious candidate would be Spain. Again - ownership of Louisiana, considered a waning but still formidable power. That said, counterfactuals aside, the utter collapse of their New World holdings and a century of backsliding makes it clear in retrospect they weren't as threatening as they might have appeared. In addition, it's known that Aaron Burr attempted to get money and support from Spain for his plans, which was one of the reasons that Jefferson tried to hang him for Treason. Had it been a nation like Luxembourg, I doubt it would have been as politically threatening.

Next, do you consider American natives a foreign power? Tecumseh's rebellion could have been considered a credible threat, especially given it's express desire to unite otherwise fractious tribes against it. Moreover, it was supported with weapons from the British. It was the British (and French) practice of arming native tribes to cause mischief that was used to justify native removals, anti-native bigotry, and generalized oppression throughout the 1800's.

The obvious worst fear would be that Britain, France, or Spain would attack and incite widespread native attacks simultaneously. Imagine, for a moment - if Tecumseh had delayed his rebellion until the War of 1812, and if Napoleon had lost in 1813, allowing Britain to turn their entire might towards the fledgling United States alongside a large-scale Native uprising?

Of course, another real problem was that Americans were, to be blunt, full of themselves, and instigated conflicts with France (Quasi War), and Britain (War of 1812) that were ill-advised. Moreover, under the Articles of Confederation, the country was barely able to stop farmers revolting over alcohol taxes.

A good barometer for American braggadocio would be Jefferson: “The acquisition of Canada this year, as far as the neighborhood of Quebec, will be a mere matter of marching; & will give us experience for the attack of Halifax the next, & the final expulsion of England from the American continent.” - Thomas Jefferson to William Duane, 4 August 1812

America enjoyed a great protection from Europe, in the form of the Atlantic Ocean, and to an outside observer, may have occasionally seemed determined to try their best to dare someone to overcome it.

During the cold War the USSR had considerable military might which was held in check by America and NATO also having sizable forces. If this hadn't been the case, would the USSR had the will to conquer?

I just realized that I forgot this part.

The USSR had formidable land military might, but never really invested in a fleet that could challenge US Naval might on the open seas. Their doctrine was to close the Atlantic with subs, and use their surface fleet to keep the US Navy out of their back yard. The USSR naval goal, in a conventional war with the US, would have been to try and cut off the Atlantic, and the key word there is try.

No one on earth, post WWI, has had a navy large enough to beat the US Navy and the stateside US Air Force contingent and manage a sustained invasion. Post WWII, either the Atlantic or Pacific fleet alone can take pretty much any nation's navy. If a war went nuclear, well then that kinda changes the whole calculus.

What about modern day, like red dawn style where they invade