No.
In both my start-ups, I was the only founder to contribute cash. It didn’t matter.
Yes, you need money. But writing code, bringing in the first customers, raising seed funding, recruiting the team, and almost anything else is more important than money.
And many times even a small investment will be very stressful for some co-founders. If your cofounder has no savings at all, don’t add to her woes if you don’t have to.
However, whoever contributes cash should usually either be repaid, at least partially, or get extra equity for that investment.
The first time I did this, I was repaid fully when we raised outside capital.
The second time, I was repaid in part when we raised outside capital.
The third time, I converted that money into more equity. I made 12x on that investment. That was the best one of all.
