Paul K's Strange Logic

In an October 12th Post [1] entitled "Foreigners and the Burden of Debt," Paul Krugman made the following comment.

. . . we'd all agree that deficits make us poorer if they crowd out investment spending, which they would if the economy were near full employment, but won't if we're deeply depressed. All we have to do is realize that net foreign investment purchases minus sales of assets from and to foreigners is also a form of investment. Or to put it a bit more simply, sure, budget deficits can make us poorer as a nation if they lead to bigger trade deficits.

I have to say I have a bit of a problem understanding this one. Let's assume we're in a depressed state as we are now and the Government decides to run an additional $1 Trillion deficit, without, for simplicity, any corresponding debt issuance. Then, assuming that the private sector saves at the rate of 6% of GDP and the trade deficit is 4%, and, neglecting any fiscal multiplier, the additional Government deficit adds $900 Billion in aggregate demand to the US economy, $60 Billion immediately to savings, and $40 Billion to the foreign sector. So, the Government deficit spending has certainly made both the domestic non-Government sector, and the foreign sector richer in USD nominal wealth, though the domestic government sector has been made 24 times more wealthy than the foreign sector.

Of course, if we take into account the fiscal multiplier on the $900 B deficit, and we assume that the Fed will add to the money supply as necessary during the ensuing economic expansion, then that 900B deficit might end up adding as much as $2.7 Trillion in GDP to the economy if it's spent in the right way. So how has this made us poorer?

Maybe Paul K has real wealth in mind in the quote and not nominal wealth. So, would the $40 Billion in increased trade deficit decrease out real wealth? I don't see how, since in a trade deficit we send USD to the foreign sellers in return for real wealth, thus increasing the real wealth held by Americans. But maybe I'm missing something about the logic of the IS-LM model?

So, how, again, can budget deficits that increase trade deficits make us poorer?

(Cross-posted from New Economic Perspectives [2].)