Minnesota Senator Amy Klobuchar was caught wearing a T-shirt emblazoned with the phrase, "You are doing a good job," amid the federal government shutdown, but she wasn't talking about herself.

Instead ... Klobuchar wore the shirt for a bunch of students while attending a high school event held at the University of Minnesota in Minneapolis, MN on Friday morning.

Check out these photos, obtained by TMZ ... the democratic Senator is standing on stage giving a speech during a robotics competition as the now-43-day partial government shutdown, which targets the Department of Homeland Security, wages on in Washington, D.C.

In a social post Friday, Klobuchar said she "caught the first flight out" of D.C. after "voting late into the night" ... before praising the students involved in the competition she attended -- adding, "as you can see from my shirt, they are doing a good job!"

Just to recap ... The House of Representatives on Friday night passed short-term legislation to fund DHS.

House Republicans hatched a plan to fund the entire department for 60 days, including Immigration and Customs Enforcement and the Transportation Security Administration.

That's the good news. The bad news is the issue now goes back to the Senate, which has just gone on recess for two weeks. Making matters worse, Senate Democratic Minority Leader Chuck Schumer has already called the plan "dead on arrival" because dems want immigration reform.

The political battle over DHS funding has left many federal employees without a paycheck for weeks, causing them to take drastic measures to survive. Some have even sold their own blood to keep a roof over their heads. But President Trump has signed an order that could start cutting checks to TSA workers as early as Monday.

Meanwhile, D.C. politicians like Senator Marsha Blackburn are slinking out of the nation's capital to enjoy spring break or, in the case of Klobuchar, heading back to high school.

We reached out to Klobuchar's rep ... so far no word back.

BTW, as you know ... TMZ wants you to send us any pics of Congress members enjoying their vacation while other federal department employees continue to go without a paycheck.