Indeed, much of the impact won't be felt for weeks or more than a month; others, like possible teacher layoffs, wouldn't take place until the new school year in the fall.
And yet, the next likely showdown — the expiration of a six-month spending bill on March 27, with its built-in threat of a government shutdown — will loom before that, meaning that the leverage the White House would hope to have won't materialize until late.
Polls also show that the public is not as engaged in this showdown as it has been in past fiscal confrontations and an NBC-Wall Street Journal Post survey indicates that Obama has lost some ground with the public in his handling of the economy.
Still, White House officials also say they believe Republicans will once again give way to additional tax revenue in part to avoid drastic cuts and in part to win reductions in Medicare and Social Security spending from Obama that they have been unable to get from Democrats before.
"I am prepared to make some tough decisions, some of which will garner some significant frustration on the part of members of my party, but I think it's the right thing to do," Obama told top business executives this week.
Given Washington's entrenched partisanship, Obama's effort could be dismissed as either another failed attempt at negotiations or as simply an effort to lay blame on Republicans for blocking compromise.
The odds aren't with the president.
Many conservatives are willing to accept the automatic cuts as the only way to reduce government spending, even though the budget knife cuts into cherished defense programs. Likewise, many liberals are beginning to embrace the cuts as a way to protect revered big benefit programs that have long been identified with the Democratic Party.