Barack Obama warned on Saturday of a "ripple effect" through the US economy that would cost hundreds of thousands of jobs after he reluctantly signed an order to begin a huge $85bn (£56bn) programme of government cuts.

The president even called the act "not smart" on the morning after the cuts officially became government policy, in a move that has been dubbed "sequestration" and has plunged Washington into another political crisis.

"The pain will be real. Many middle-class families will have their lives disrupted in a significant way," Obama said in his weekly address. He added that up to 750,000 jobs could be lost and half a percentage point knocked off America's economic growth this year. "This will cause a ripple effect across the economy. Businesses will suffer because customers will have less money to spend ... These cuts are not smart. They will hurt our economy and cost us jobs," he said.

The sequester originates in a political crisis in 2011, when debates over deficit reduction almost saw the US government default on its debt payments. To avert that crisis, Democrats and Republicans agreed that, unless they struck a deal on shrinking the country's debt, then the cuts to federal spending would begin.

The idea was that the prospect of cuts to social services would motivate the Democrats and hurting military spending would do the same for Republicans. Instead, despite the looming deadline last week, no grand bargain was ever struck and the cuts – which neither side had intended to happen – are now coming into force and spreading throughout the federal government. Over the next 10 years they will represent $1.2tn of slashed spending.

The hardest-hit part of the government will be the Pentagon, which has to make $40bn of cuts between now and September – about 9% of its budget. Defence chiefs have already said that the move will delay deployments – such as a recent move of an aircraft carrier to the Gulf – and hurt national security.

But almost every government department, from aviation to the park service, will be hit, with cuts amounting to about 5% of their overall budgets. Only Medicaid and welfare benefits such as food stamps are exempted. The Federal Aviation Authority has said that it will have to close scores of air traffic control towers and the National Labour Relations Board has already given staff 30 days' notice that they could be suspended from their jobs. Over the next few weeks, more such letters will go out, threatening school services and the smooth running of scores of other government functions.

In his speech Obama blamed Republicans for inaction, saying that their hostility to any sort of extra tax revenues being generated from rich Americans was the root cause of the problem. In recent weeks, and since his victory over Republican challenger Mitt Romney in last year's election, Obama has not shied away from attacking his opponents as defenders only of the wealthy.

"It's happening because Republicans in Congress chose this outcome over closing a single, wasteful tax loophole that helps reduce the deficit. Only last week they decided that protecting special interest tax breaks for the well-off and well-connected is more important than protecting our military and middle-class families from these cuts," Obama said.

But Republicans only want cuts on welfare spending, rather than defence, and have insisted on no new taxes. Republican House speaker John Boehner, at the end of the White House talks on Friday, was adamant that he will not contemplate any new taxes: "The discussion about revenue is over." That hard line is popular with his party's rightwing base but has left the party vulnerable to being attacked as being too entrenched in its ideology – especially after Obama's resounding victory in 2012.

In seeking to lay the blame for the sequester at the doors of the Republicans, the Obama administration has run a carefully orchestrated image campaign aimed at focusing on the impact on middle-class American workers and their families. Obama continued that theme on Saturday, saying Republican leaders were out of touch with ordinary people and their own voters. "We just need Republicans in Congress to catch up with their own party and the rest of the country," he said.

But on Saturday Republicans were holding firm. Washington congresswoman Cathy McMorris Rodgers criticised out-of-control government spending and said there was no point in new taxes as the money would be wasted. "Instead of campaigning for higher taxes, the president should lead an effort to begin addressing our nation's spending problem," she said.

But for many observers the fiasco of the sequestration – which in effect means both parties are implementing a policy that neither wants and each thinks is damaging – has left many complaining about a broader American political dysfunction. Yet the sequester is only one of several rolling crises that are threatening the smooth running of the world's biggest economy that is still stuttering to recover after the Great Recession.

If Congress does not reach an agreement on a budget for this year by 27 March, the federal government faces the prospect of shut-down. Soon after that, Congress has to approve an increase in the federal debt limit: the same move that two years ago created gridlock in Washington and resulted in the sequester. The House of the Representatives is due to vote next week on a deal to prevent a federal shutdown but there is a risk this could end up in a new standoff between the Republican-controlled House and the Democratic-controlled Senate