BRIDGEPORT, Conn. — In his final campaign swing, President Obama rallied voters Sunday in Connecticut and Pennsylvania for Democratic gubernatorial candidates, but his first rally of the day was interrupted several times by protesters demanding more lenient immigration policies.

Mr. Obama’s event for Gov. Dan Malloy at a high school in Bridgeport, Connecticut, was roiled at the start by incidents of people heckling him and forcing him to stop his prepared remarks. Police hauled two young men out of the crowd after they repeatedly shouted down the president. One was wearing a T-shirt that said “Obama Deports Parents.”

“The Republicans are blocking immigration reform,” Mr. Obama said. “That’s one more reason we need a Democratic Senate.”

After the young men were led away, Mr. Obama said, “Let’s try again.” But a few moments later, a woman started screaming at the president.

Mr. Obama again halted his speech to say “I am sympathetic” to people complaining about the lack of immigration reform in Congress.

“That’s why we fought for immigration reform,” he said. “It’s the other party that’s blocking. Unfortunately, folks get frustrated, and they yell at everybody.”

At another point, Mr. Obama said, “Republicans are patriots. They love their country.”

“No, they don’t!” a man shouted.

“Listen, just because folks are good folks doesn’t mean they’ve got good ideas,” Mr. Obama replied.

Near the end of his speech, he was interrupted by another protester, but the crowd drowned her out with (constitutionally impossible) shouts of “Four more years!”

The immigration group called United We Dream said “dreamers” from Connecticut, Florida, Massachusetts and New York confronted Mr. Obama as he gave his speech.

“Dreamers will not take any more political delays or excuses,” said Maria Praeli of Connecticut, a member of the group. “Our community expects President Obama to be broad in using his executive authority to provide deportation relief to millions of people from our community, including parents of dreamers, and we’re here to hold him accountable to his promise.”

The president is planning to issue an executive order after Election Day to allow a significant portion of the estimated 11 million illegal immigrants to remain in the country.

Mr. Malloy is in a tight race with Republican Tom Foley, in a rematch of their 2010 campaign that Mr. Malloy narrowly won.

In Pennsylvania, businessman Tom Wolf is leading Republican Gov. Tom Corbett, who received some help Sunday with an appearance by New Jersey Gov. Chris Christie.

At a rally at a high school in Bridgeport, Mr. Malloy raised the memory of the school shootings in Newtown, Connecticut, in December 2012 and said Mr. Obama “cared about us.”

“He came to our state just a few days later,” Mr. Malloy said. “And he gave one of the most compelling speeches about who we are and what we are.”

Mr. Obama’s final campaign appearances ahead of Tuesday’s critical midterm elections continued his pattern of visiting states that he won in 2012 and 2008 and stumping almost exclusively for gubernatorial candidates. Senate Democrats are shunning Mr. Obama, who is especially unpopular in Republican-leaning states such as North Carolina, Arkansas and Georgia.

The president stumped for Mr. Wolf on Sunday night at Temple University in Philadelphia, the state’s biggest Democratic bastion.

On Saturday night, Mr. Obama told Michigan voters that they must vote if they hope to change the status quo in Washington.

Mr. Obama hit the stump for Gary Peters and Mark Schauer, Democratic candidates for Senate and governor of Michigan, respectively. Mr. Peters is going up against Republican Terri Lynn Land, while Mr. Schauer is challenging incumbent Republican Gov. Rick Snyder.

At a campaign rally in Detroit, the president returned to his familiar theme of “hope” and told Democrats that they must vote to defeat the Republican establishment.

“The hardest thing in politics is changing the status quo,” Mr. Obama said. “You’ve got a lot of people in power who just care about keeping power. They don’t care about you. … They hope you don’t get involved. They hope you don’t organize. They hope you don’t vote. And every day they’re sending you a message that you don’t count. Don’t buy it.”

On Friday night, Mr. Obama rallied Democrats in Maine.

At each stop, the president takes direct aim at the Republican economic agenda, painting it as a collection of tired ideas that have been tried and do not work. He singled out Republicans’ support for tax cuts for wealthy Americans.

“It’d be one thing if we hadn’t tried them. We might say, ‘OK, maybe that works.’ But when you’ve done it again and again and each time the middle class has a tougher time and the folks at the top are doing better and better, I don’t know why we think it would work better this time,” he said.

⦁ Ben Wolfgang contributed to this report.

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