Standard and Poor's rating agency estimates that the government shutdown cost the US--the country, not the government--$24 billion. This figure is based on what the gross domestic product would have been, without the shutdown, compared with what it actually is. This is all hypothetical, of course. No one can say what the GDP would have been because no one can predict the future with certainty.
The government shutdown certainly caused loss of pay for many thousands of workers, not just federal workers, but all those whose livelihood depends on the federal government. It also caused hardship for those left without day care, or unable to get Medicare or Medicaid.
The damage done by Republicans to the US economy, however, has been much greater than just $24 billion. The great recession was a severe blow to the economy. The recession may not have been the fault of the Republicans alone, although an argument can be made that they caused more than a little of it by their obsession with government regulations, which they relaxed with disastrous consequences. But the Republicans were wholly responsible for the lack of a second stimulus package and by the false economies of reductions in government spending that have made the recovery from this recession much worse than average for recoveries in the US.
In fact, the average recovery of the US from recessions after 48 months has been 17%. At this point, the US GDP is only 9% higher than it was in December, 2008. After previous recessions, under both Democrats and Republicans, the federal government has passed vigorous stimulus, assuring that the economy would recover as quickly as possible. After the 2010 elections gave them control of the House of Representatives, the Republican congress refused to pass any stimulus at all. In fact, they forced the president to accept a seriously reduced federal budget, an action that further damaged the economy.
A simple mathematical calculation shows approximately how much the economy has been damaged by Republican intransigence. The economy has actually grown by 9%, or $880 billion since December 2008. If it had grown at a 17% rate (which is only the average rate for recoveries), it would now be $1.31 trillion higher than it actually is.
Therefore, the idiotic policies of Republicans in congress have already cost the nation at least $1.3 trillion.