The revised estimates from the Council of Economic Advisers show that the shutdown, now in its fourth week, is beginning to have real economic consequences. The analysis, and other projections from outside the White House, suggests that the shutdown has already weighed significantly on growth and could ultimately push the United States economy into a contraction.

While Vice President Mike Pence previously played down the shutdown’s effects amid a “roaring” economy, White House officials are now cautioning Mr. Trump about the toll it could take on a sustained economic expansion. Mr. Trump, who has hitched his political success to the economy, also faces other economic headwinds, including slowing global growth, a trade war with China and the waning effects of a $1.5 trillion tax cut.

To blunt the shutdown’s effects, the administration on Tuesday called tens of thousands of employees back to work, without pay, to process tax returns, ensure flight safety and inspect food and drugs. But some people involved in the shutdown discussions in the White House have privately said they anticipate that Mr. Trump will grow anxious about the economic impact in the coming days, accelerating an end to the stalemate. Others close to the president believe Mr. Trump has leverage and are encouraging him to stand by his demands.