Joe Biden amplified his attacks on Republicans over Medicare and Social Security during a visit to Florida on Thursday, arguing that it was the party’s “dream” to slash the federal programs and vowing to be the “nightmare” that stops them.

Speaking in Tampa, Biden outlined his administration’s plan to safeguard the popular entitlement programs as part of an ongoing war of words with his Republican opponents that began during his second State of the Union address on Tuesday.

Ahead of an anticipated 2024 re-election campaign, the president has seen an opportunity to put Republicans on the defensive on an issue that resonates deeply with voters, and particularly seniors who rely on the programs and are a key part of their base.

“I know that a lot of Republicans – their dream is to cut Social Security and Medicare,” Biden said, during his remarks at University of Tampa. “If that’s your dream, I’m your nightmare.”

Republicans have flatly rejected the assertion, despite a long record of proposing to do just that. During the midterms, several prominent Republicans opened the door to Medicare and Social Security cuts as part of their effort to reign in the federal budget.

Many Republicans have accused Biden of lying about their fiscal agenda. House Speaker Kevin McCarthy said this week that cuts to Medicare and Social Security were “off the table” as part of any plan to reduce the nation’s debt.

Their objection to the accusation on Tuesday night – loud howls from the chamber and shouts of “liar” – prompted a remarkable back-and-forth during the State of the Union, in which Biden paused to engage his hecklers. “Liar!” screamed the congresswoman Marjorie Taylor Greene, a Republican of Georgia.

Recalling the exchange, which he referred to as a “spirited debate”, Biden boasted that he had extracted assurances from them that they would not cut the programs. “Granted, I’ll believe it when I see it,” he told the audience on Thursday, as he highlighted individual Republican plans that he said would make the programs more vulnerable to budget cuts.

Among them was an idea put forward by the Republican senator Rick Scott of Florida, who proposed sunsetting nearly all federal spending programs after five years. Holding up a pamphlet with the senator’s plan, Biden said subjecting Social Security and Medicare to periodic renewal votes would raise the likelihood of dramatic cuts.

“The very idea the senator from Florida wants to put Social Security and Medicare on the chopping block every five years I find to be somewhat outrageous – so outrageous that you might not even believe it,” he said.

In a tweet welcoming Biden to Florida, Scott accused the president of “lying to Floridians about Social Security and Medicare” and challenged him to a debate on the issue.

Responding to the senator’s pushback, Biden quipped: “Maybe he’s changed his mind; maybe he’s seen the Lord, but he seemed to want a sunset.”

Despite vehement protests, Republicans have not yet said how they plan to reduce spending to meet their goal of putting the US on a path toward a balanced budget. Without touching those programs, which alone count for a substantial piece of the nation’s federal budget, it is unclear how they would meet that objective without making painful cuts to defense spending or raising taxes, options many Republicans have categorically ruled out.

Biden has appeared to relish sparring with Republicans over the issue, which the White House has long seen as politically potent. Democrats tried to wield the issue against their opponents in the November midterms, but they struggled to rally voters against the hypothetical cuts despite a better-than-anticipated performance.

Many Democrats now believe that changed on Tuesday, when Americans saw the debate unfold in primetime. Biden departed the House chamber confident he had bested his political foes, just as he intends to seek a second term. A formal announcement is expected sometime this spring.

But recent opinion polls show Biden struggling to unite Americans behind his agenda, with few giving him credit for his legislative accomplishments. Most voters, including a majority of Democrats, say they would prefer someone else to be the party’s standard-bearer in 2024, though a primary challenge has become increasingly unlikely.

With 2024 coming into focus, Biden brought his message to Florida, once the consummate presidential battleground that has slipped from Democrats’ reach in recent elections. It is also home to a large retiree population and two of the president’s potential 2024 Republican rivals: Donald Trump, who announced his candidacy shortly after the November midterms, and Florida’s governor, Ron DeSantis, who won re-election by a dominating 19 percentage points in November.

Targeting DeSantis, Biden called on the governor to expand Medicaid in the state, estimating an additional 1.1 million Floridians would be eligible for the program.

“This isn’t calculus,” Biden said. “The only reason Medicare expansion hasn’t happened here is politics.” He also repeated his calls for Congress to raise taxes on the wealthiest households and corporations as well as to extend a $35 monthly cap on the cost of insulin to all Americans.

In a statement ahead of Biden’s visit, Ronna McDaniel, chair of the Republican National Committee, said the president’s plans to rebuild the economy were “too blissfully out of touch to care”.

The visit was the second stop on his post-State of the Union “blitz”, which has seen the president, vice-president and cabinet officials travel the country to promote his administration’s legislative agenda. His first stop was at a union training facility in Wisconsin.