The White House has been struggling to highlight cutbacks at federal agencies now that the so-called sequester has hit. On Tuesday, it found one close to home.

Tours of the executive mansion will be canceled starting Saturday, the White House announced, citing “staffing reductions resulting from sequestration.” The tours will not be rescheduled and the freeze will be in effect “until ­further notice.”

The cancellation will annoy plenty of tourists who tour the White House after securing their tickets well in advance through their elected representative’s office. It also will certainly annoy those congressional offices that must begin notifying disappointed ­constituents.

“We very much regret having to take this action, particularly during the popular spring touring season,” the White House said in a recorded message on the tour hot line.

Within hours of the announcement, Republicans began to criticize the decision as a stunt. One GOP congressman offered his own solution to the budget ­cutting at the White House. In an amendment to a bill to fund the government, Texas Rep. Louis Gohmert proposed that none of the money “may be used to transport the president to or from a golf course until public tours of the White House resume.”

In the lead-up to the automatic budget cuts, which kicked in on Friday, the White House tried to pressure Republican lawmakers to reach a deal by highlighting the pain that would come from axing federal services. But its top spokespeople on the matter occasionally overstepped.

Education Secretary Arne Duncan on Monday apologized for saying that teachers in a West Virginia school district were receiving “pink slips” because of the budget cuts. The district’s superintendent told the Washington Post that the teachers were receiving transfer notices and the move was not directly related to the federal funding cuts.

Republicans pounced on Duncan’s comments and other claims as examples of the president hyping the cuts for political gain. On Tuesday, the news of the canceled tours prompted similar skepticism among some on the Hill and the GOP-led House Administration Committee offered tourists an alternative: “House Admin welcomes Americans visiting D.C. to tour Capitol instead,” the committee tweeted.