WASHINGTON — First the White House and Congress created a potential fiscal crisis, agreeing more than a year ago to once-unthinkable governmentwide spending cuts in 2013 unless the two parties agreed to alternative ways to reduce budget deficits.

Now that those cuts are imminent — because compromise is not — they have created one of Washington’s odder blame games over just whose bad idea this was.

The battle lines over cuts that are scheduled to begin on Friday, known in budget parlance as sequestration, were evident on Saturday in President Obama’s weekly address and the Republican response, by Senator John Hoeven of North Dakota.

“Unfortunately, it appears that Republicans in Congress have decided that instead of compromising, instead of asking anything of the wealthiest Americans, they would rather let these cuts fall squarely on the middle class,” said Mr. Obama, who proposed a substitute mix of spending cuts and revenues from repealing some tax breaks for wealthy people and corporations.