I don't believe this cartoon was promoting a "war tax" specifically, but rather that it emphasized that paying taxes was a patriotic way to support the country.
I agree with yglesias:
... the cartoon does drive home the basic points that war costs money and things that cost money require taxes. Taxes were a hard sell then and they’re a hard sell now. But the way the sale was made in ‘43 was to convince people that the war was worth the cost. These days, politicians seem to feel that the public would refuse to pay for the war if asked plainly. So instead of asking, they try to obscure the cost.