This beats the 21-day shutdown which took place in 1995-6 when Clinton was President.
President Trump is refusing to sign a finance bill unless Congress provided him with $5.7billion (£4.5billion) for a wall along the US-Mexico border, which Democrats are resisting.
Some 800,000 US Government employees are currently unpaid.
On Friday workers missed out on what would have been their first salaries of the year.
Trump has threatened to call a national emergency to provide funding if Democrats continue his opposition.

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He said on Thursday: “If they can’t do it I will declare a national emergency. I have the absolute right.”
Democrats have said they plan to mount legal challenges should he take such action.
On Friday the House and Senate passed a bill designed to ensure government workers are paid retroactively when the shutdown ends.
Trump is expected to approve the plan.
On Friday workers missed out on what would have been their first salaries of the year.
Trump has threatened to call a national emergency to provide funding if Democrats continue his opposition.
He said on Thursday: “If they can’t do it I will declare a national emergency. I have the absolute right.”
Democrats have said they plan to mount legal challenges should he take such action.
On Friday the House and Senate passed a bill designed to ensure government workers are paid retroactively when the shutdown ends.
Trump is expected to approve the plan.
Justifying the need for funding for the wall in an Oval Office address on Tuesday, the President said: “This is a humanitarian crisis – a crisis of the heart and a crisis of the soul.”
He added: “My administration has presented Congress with a detailed proposal to secure the border and stop the criminal gangs, drug smugglers, and human traffickers. It’s a tremendous problem.
“Our proposal was developed by law enforcement professionals and border agents at the Department of Homeland Security.
“These are the resources they have requested to properly perform their mission and keep America safe.”
However, Senior Democrats have accused Trump of governing by “temper tantrum” in refusing to sign off on a budget which does not include funding for the border wall.
They are demanding he reopens the government and holds separate discussions on his immigration policy.
The President has said he will not budge on his demands and is willing to allow the shutdown to continue for “months” if required in order to get his funding.
More to follow…