WASHINGTON — On the endgame for the budget showdown looming in Washington this fall, only this is clear: President Obama thinks Republicans cannot risk another debt crisis or government shutdown, and Republican leaders agree.

That consensus suggests that the odds of an economy-damaging stalemate are relatively low, despite rising jitters in the capital. Yet everything else about how the White House and Congressional negotiators will try to strike a deal, and then coax majorities to approve it, remains opaque.

“Even those of us quite close to it have a hard time saying how the movie ends,” said Representative Chris Van Hollen of Maryland, the ranking Democrat on the House Budget Committee.

The showdown encompasses three interlocking fiscal disputes that will challenge Mr. Obama and his Republican interlocutors to bridge seemingly irreconcilable goals.