WASHINGTON, May 6— ''The budget document is just a political
document,'' said Senator Paul Laxalt. ''As soon as we adopt one,
it's quickly forgotten.''  It is true that old budgets do not
make popular bedtime reading. But the annual ritual of adopting
a spending plan for the Federal Government tells more about the
politics and priorities of Congress than any other event on the
legislative calendar. And this week the unsuccessful efforts of
the Senate Republicans to adopt a budget have divided them into
three unhappy and unyielding factions.  This fragmentation
reflects the evolution of the Republicans from minority to
majority status, from outsider to insider. For the last
generation, they have been the critics of the legislative
process, not the architects of it, and they are not used to the
compromise and accommodation that make that process function
smoothly.  ''It's a different experience for us, so it's been
difficult,'' said Senator Richard G. Lugar, Republican of
Indiana. Senator Charles E. Grassley, R