The common ground:
* The government of Japan faces budget constraints; it cannot tax more than a certain amount and that includes seigniorage (taxing using inflation).
* Right now Japan doesn't seem to be immediately close to those constraints since interest rates and inflation are low.
* Lowering taxes, spending more and depreciating the currency will expand the economy, but rates will increase and so will inflation (among with wages).
* Inflation expectations can create actual inflation. It can be generalized that different people will demand higher prices in advance if they can, since they know their costs will rise. The same applies to interest rate and there is a link between them (investors demand higher yields if inflation is expected).
* Default and excessive inflation can be a result of too much expansionary policy (eventually, what is too much is up for debate), but they can destroy the gains and make the economy worse off.
The disagreement (you can see that its actually a spectrum of opinion and there are differences between the details of the policies, but for clarity I've divided them neatly into two camps):
* School A believes expansionary policy will make Japan default because the government will have lost control, since expectations can make interest rates and inflation jump rapidly. They site that the level of Debt to GDP is over 200% as evidence. They say the government should not lose credibility or else.
* School B believes that the expansionary policy is so hard to actually pull off that some expectations of inflation and higher rates are desirable. Since rates stay low and deflation is always around the corner it seems that the government can easily reverse too much expansionary policy, far before a default appears to be likely. Additionally Increased GDP will bring more revenue, decreasing the need to rely on inflation after a certain point. They joke that the "government should credibly promise to be irresponsible" to get out of the bad equilibrium that is the lost decades.
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A political compromise appears to have been made by mixing expansionary policy with the decision to increase the sales tax. Since this caused a recession school B feels vindicated - getting to a default and inflation path is really hard. Interest rates and inflation refuse to bulge.
However the lack of progress will add even more to the debt to GDP, perversely aiding school A (even thought some of them might agree that B were right in the previous period). So the end result has been 20 years of the government oscillating between those two positions, without reaching a point where either side can victory (default or significant GDP growth).