Are you sure your graphics hardware is the limiting factor?
On my elderly Thinkpad X220 with Intel HD 3000 graphics, I'm able to sustain an SDL2 framerate greater than 60fps, as tested with
this tutorial.
(I needed to install sdl2-image and sdl2-ttf, and build with $ g++ -w -L/usr/local/lib/ -lSDL2 -lSDL2_image -lSDL2_ttf -L/usr/X11R6/lib -I/usr/local/include/SDL2 -o test 24_calculating_frame_rate.cpp)
Edited to add: oh, yes, you have a 6-core Haswell processor, NVIDIA graphics, and you're using VESA, which limits your framerate.