@dave r said:

The downside to this window resizing is that it often scrambles toolbars.

he's claiming mac so the toolbars shouldn't be a problem..

the reason your drawing is spilling out onto multiple printed pages is because you have borders set up in your paper preferences… sketchup considers these borders as part of the drawing which leads to the spill.. (bad sketchup! bad 😉 )
[EDIT].. well, actually, it doesn't consider the borders as part of the drawing.. so it will calculate the scale for the entire sheet of paper then once the print happens, the boarders have been added to the info provided by sketchup (i.e.- if you set up in sketchup for an 8.5 x 11 print but you have 1/4" borders designated, the printer sees that you're trying to do a 9x11.5" print so it spreads it across multiple sheets.. if that makes any sense 😉 )

go File -> Page Setup…

then click the 'paper size' drop down.. if your selected printer has borderless options available in your desired paper size, choose that.. otherwise, click on 'Manage Custom Sizes…' and enter desired paper size but leave all the borders at 0..
it will prevent your spillage..

i have an applescript which will resize your sketchup window to the same aspect ratio as your chosen paper.. it will then zoom the drawing window to the maximum allowable scale for your paper size and drawing (i.e.- it will show the window as, say, 1/4" = 1' then give the option to zoom to a smaller scale if desired (if you go bigger, the drawing won't fit on the single page so that's not an option)) …. i didn't post the script publicly because i soon found out that older OS's need adjustments in order to work and getting that type of compatibility was harder (or definitely less exciting) than making the script work in the first place..