Whitespace after the , causes the shell to parse your expression as two separate tokens, instead of as a brace expansion:

$ printf '%s

' {"File 1", "File 2"}.txt

{File 1,

File 2}.txt

You just need to remove the whitespace:

$ printf '%s

' {"File 1","File 2"}.txt

File 1.txt

File 2.txt

So

$ touch {"File 1","File 2"}.txt

$ ls

'File 1.txt'  'File 2.txt'

More compactly, you could also use touch "File "{1,2}.txt or touch File {1,2}.txt