Following remarks on his attempts to build out a "hollowed" middle class, Biden shifted to discussing his goal of making billionaires and corporations pay more in taxes.

"Corporations ought to do the right thing … That's why I propose that we quadruple the tax on corporate stock buybacks to encourage long-term investments instead."

"Let's finish the job and close the loopholes that allow the very wealthy to avoid paying their taxes," he said, urging Congress: "Reward work, not just wealth. Pass my proposal for a billionaire minimum tax."

House Speaker McCarthy, however, has pushed back. He said on Monday when speaking on the debt ceiling: "Defaulting on our debt is not an option but neither is a future of higher taxes."

Biden's new proposal comes after a sticking point in the Inflation Reduction Act's passage, a 1% excise tax on share buybacks that was added to the landmark bill in order to move forward.

Democrats stripped from the bill a tax break favoring wealthy hedge-fund managers called the "carried interest loophole" before its passage.

Biden may still be some ways from formally declaring his intentions about a 2024 reelection campaign, but his message on Tuesday -- he wants to "finish the job" -- certainly hints at another bid.

Yet this comes in the face of polls that have shown an unusually high percentage of Americans don't want him to run again -- including Democrats. In a new ABC News/Washington Post survey, 58% of Democrats said they wanted the party to nominate someone other than Biden, a finding echoed by a recent AP/NORC survey, too. Now, it's not unheard of for the public to prefer that a president not run again. For instance, majorities told pollsters at different points in 1982 and 1983 that they didn't want Ronald Reagan, another older president, to run again. But in those polls, a majority of Republicans still wanted four more years of Reagan, in contrast to what Democrats are saying in polls about Biden.

However, none of this means Biden will be an underdog in the 2024 Democratic primary. Fact is, elected presidents rarely face serious opposition for renomination. Importantly, Biden has a solid approval rating among Democrats -- around 80% for better in most polls -- so while many Democrats express skepticism toward another Biden run, most also don't mind how he's governing the country. This complicates any would-be challenger justifying a campaign against Biden.

Moreover, the potential Democratic candidates polling best against Biden are in his administration -- Vice President Kamala Harris and Secretary of Transportation Pete Buttigieg -- making them unlikely to run against him. Although we can't discount someone from the left taking on Biden, the leftward threat posed by Vermont independent Sen. Bernie Sanders faded when he encouraged the party to coalesce around Biden ahead of Super Tuesday in 2020 -- before Biden was the clear leader of his party. Barring a major collapse in Biden's standing, then, a serious primary challenge appears unlikely.

-FiveThirtyEight's Geoffrey Skelley

Noting he has seen firsthand the devastation from record floods, storms and wildfires, the president discussed efforts to prepare for the long-term -- such as building electric grids, roads and water systems to help weather the next big storm and flood.

"Let's face reality. The climate crisis doesn't care if your state is red or blue. It's an existential threat," Biden said. "We have an obligation to our children and grandchildren to confront it."

"We're still going to need oil and gas for a while, but there's so much more to do," he continued.

After touting his administration's victories on the economy, Biden spoke about the concerns that he said Americans have about about health care.

"For example, too many of you lay in bed at night staring at the ceiling, wondering what in God's name happens if your spouse gets cancer or your child gets deadly ill or if something happens to you," he said. "Are you going to have the money to pay your medical bills? Are you going to have to sell the house?"

Biden said his administration is bringing costs down so "you can sleep better at night" -- including measures to cap the cost of insulin for seniors on Medicare and give Medicare the power to negotiate drug prices and enhanced Affordable Care Act subsidies that has lowered premiums.

Still, he said there is more work to do, like capping insulin prices for all Americans who need it and extending the lifespan of benefits.

"Let's finish the job, make those savings permanent and expand coverage to those left off Medicaid," he said.