President Obama arrives at Selfridge Air National Guard Base on Sept. 9, 2015, in Harrison Township, Mich. (Andrew Harnik/AP)

President Obama issued a warning to Congress on Wednesday over the looming budget deadline, saying it would be “wildly irresponsible” if the government shuts down at month’s end over a failure to approve a federal spending plan.

With Republicans facing internal divisions over how to move forward, Obama traveled to Macomb Community College here to rally support for his administration’s efforts to increase federal investments in education and job training programs.

“We’ve got Republicans in Congress who are going in the opposite direction,” Obama said. “Some are even talking about shutting down the government at the end of the month.” He added: “There’s a lot of talk about that in Washington, for unrelated reasons that, by the way, don’t even have to do with the budget. They have to do with politics and presidential elections and posturing.”

Obama’s roadshow — he visited Boston on Monday to tout a new executive order to increase paid sick leave for federal contractors — comes as the administration is aiming to draw a contrast with the president’s economic agenda and that of his Republican rivals in an election season.

Inside the White House, however, there is growing alarm that the congressional fight over the budget could result in the second shutdown in three years, after the government was shuttered for 16 days in 2013 over Republican opposition to Obama’s health-care law.

GOP leaders in both chambers have vowed not to repeat that process. But conservatives led by Sen. Ted Cruz (R-Tex.), a presidential candidate, have threatened to oppose a spending plan that maintains funding for Planned Parenthood. That has left the outcome uncertain as federal spending authority expires Sept. 30.

“Our economy is actually a bright spot in a pretty volatile world economy,” Obama said. “After all the hard work the American people have done to get us back on our feet to recover from that Great Recession, now’s not the time to play games.”

On this trip, the president enlisted the aid of Jill Biden, the vice president’s wife, who is an educator at Northern Virginia Community College. She joined Obama on Air Force One and joked to the crowd that she graded papers during the flight.

Ahead of the trip, the White House announced a new grant program from the Labor Department to provide $175 million in federal funding to help create apprenticeships for 34,000 people, in conjunction with additional support from the private sector.

The president, in his remarks, highlighted his State of the Union proposal to make community college free, a plan that has faced opposition from Republicans over the estimated $60 billion price tag.

Obama is intent on taking the debate “around the country,” Cecilia Muñoz, the White House’s director of domestic policy, told reporters on a conference call Tuesday previewing the event. “What we’ve seen is momentum around the country.”

Muñoz said Oregon and Tennessee have approved plans to use state funds to finance community college, and Minnesota launched a pilot program to do so this year.

The president told the crowd he was growing wistful about the prospect of his eldest daughter, Malia, a high school senior, heading off to college next year.

“She puts her head on my shoulder. She says, ‘Daddy, you know, you realize this is probably going to be the last time that you ever send me off for my first day of school,’” Obama said, prompting the crowd to reply with an “Awww” in unison.

“I had to look away, you know. I didn’t want to just be such a crybaby,” the president continued. “It makes no sense. Michelle and I are way too young to have daughters, you know, who are both almost in college now. So as a parent, I was a little freaked out.”