I can't believe what I've been seeing in the thread that Bryan started here and updated most recently here. So far, if this were a question on an intermediate macro test, nobody gets full credit.
What if you raise spending (or cut taxes) and hold the quantity of money constant?
The textbook answer, which Bryan gave but rejected, is that interest rates go up, the demand for money falls, and the fall in the demand for money acts like an increase in the supply of money--nominal GDP goes up.
Bryan questioned whether money demand responds to small changes in interest rates. Inelastic money demand (the opposite of a liquidity trap, which would be super-elastic money demand), is a weird case to think about, because it makes the Fed unable to determine the money supply. Suppose that the Fed wants to raise (lower) the money supply. Under Bryan's assumption, the only way to increase (reduce) money demand is to make interest rates fall (rise) by a huge amount. I think that the "inelastic money demand function" is neither theoretically nor empirically interesting.
Then, the discussion turned to whether fiscal policy does in fact have an impact in the U.S. I believe it was Paul Krugman who made the point that if the Fed is setting a nominal GDP target, and it sticks to that target, then fiscal policy will not affect GDP. That seems like a pretty safe tautology. But I think there was once a Sargent-Wallace paper that said that if the public expects the deficit to be monetized eventually, then a deficit could be inflationary even if today the Fed is not increasing the money supply. That paper was about 30 years ago, when rational expectations theorizing was way out of control.
One quibble is with the statement that under a nominal GDP target a fiscal expansion causes complete crowding out. True enough in a closed economy. But in an open economy, some of what gets crowded out could be net exports, not just private investment. So, an expansionary fiscal policy reduces private investment and/or increases private saving and/or increases foreign saving (the trade deficit). But in any case, the fiscal expansion gets offset somewhere, because the Fed makes sure of that.
All that is textbook stuff. Getting away from that, I would say that in my own mind, the Fed is not the main actor here. The key interest rates in the economy are long-term rates, set in the bond market. What Ed Yardeni once dubbed the "bond market vigilantes" are the ones setting GDP targets. The Fed is more like the Wizard of Oz--someone everyone wants to believe is all-powerful, but which really isn't.
In general, my views of macro have shifted in the direction of the "attribution error" model. That is, we don't really understand economic fluctuations, and I think that what we attribute to fiscal and monetary policy is more than what they actually account for.
I have a suspicion of macroeconomic models that is analogous to my suspicion of climate models. I think that the data are not powerful enough to answer the most interesting and important theoretical questions, so a lot of debates just stay unresolved forever.