You can absolutely use your 120v generator and have 240v. What you are looking for is called an autotransformer, sometimes shortened to autoformer. One I would recommend is made by Outback Power, the PSX-240. I'm sure there are others.
To answer your question about phase angle, the 2 hot legs of a 240/120v split phase service are 180 degrees out of phase.
By using the PSX-240 and a PROPER TRANSFER SWITCH you can have 240v available in your panel form your 120v RV generator.
As anyone with a deep well pump knows, often have 240v to run the well pump is one of the most important loads a generator might be needed for.
The suggestion of feeding both legs of the panel the same phase is not a good one if your house has any multi-wire branch circuits. These can be identified by a cable containing a red wire in addition to the black, white, and bare ground. Supply both the black and the red with 120v from the same leg of a generator can cause the neutral wire to carry excessive current leading to overheating.