Curious Stuffs - New Keynesian model is same as Neo-Fisherian in ZIRP?

From a paper in 2009 by Gauti Eggertsson, a staff of NY FED, a very distinguished New Keynesian economist:

Tax cuts can deepen a recession if the short-term nominal interest rate is zero, according to a standard New Keynesian business cycle model. An example of a contractionary tax cut is a reduction in taxes on wages. This tax cut deepens a recession because it increases deflationary pressures. Another example is a cut in capital taxes. This tax cut deepens a recession because it encourages people to save instead of spend at a time when more spending is needed.

Via the Money Illusion,

Elsewhere he showed that in a deep depression, the NK model suggested that artificial attempts to raise wages, such as FDR’s NIRA, could be expansionary.
Several economists have recently suggested that the NK model has NeoFisherian implications. If the Fed were to raise its fed funds target, the policy shift would be inflationary.

Eggertsson's logic is very clear.
AD curve has downward slope to the right normally because higher inflation causes tighter monetary conditions and decreased investment and personal consumption.

However, given nominal rate, for example it's zero, for a long time, households must increase to spend their money only if the inflation is expected to be robust, because it pushes real interest rate lower and makes current consumption cheaper than next. So, AD curve becomes upward slope-shaped.

On this AD curve, tax cut policy, for example, should lead the deflationary pressure, because;

1) AD curve is not affected by that. It means curve location remains. It's because households and companies only react on inflationary pressure given nominal rate for longer period.
2) AS curve moves down. It's the key. It's because more people may participate labor market for expecting more disposable income.
3) But, on the AD curve, people will face the headwind of declined "real" wage.
4) And so, the real economy will be suffered from deflationary pressure.

So, if we want to boost real economy, short-term interest rate should be raised. This should change the slope or shape of AD curve from downward to upward. (Below chart showed inverted case)

If then, the first movement of U.S. Fed would be much more significant for real economy than market participants expect...!!

If given nominal rate condition, unfortunately, fiscal policy, especially increasing government spending would be more powerful tool. Fiscal multiplier could be more than 1.0 in contrast of normal AD-AS model's lower than 1.0 caused by crowding out effect.

It's so curious and funny because this consequence is equal to Neo Fisherian's. The aspect of possible inflationary pressure even from Fed's fund rate hike or/and increasing arguments that fiscal expanding is need would be main theme next year's financial market.

And more likely, we should focus on whether the economic dynamics change from deflation to normal-inflationary environment as FED starts monetary tightening...!