BALTIMORE — President Joe Biden said Thursday he is confident about getting his major infrastructure and social spending packages through Congress, but downplayed chances of securing his aim for a higher corporate tax rate.

“I do think I’ll get a deal,” Biden told a town hall with a live audience on CNN.

Biden said his feuding Democratic party was “down to four or five issues” but “I think we can get there.”

Democrats have razor-thin majorities in both houses of Congress. However, internal divisions are preventing passage of a $1.2 trillion infrastructure revamp and a huge, separate social spending bill that Biden says will transform finances and fairness for ordinary Americans.

With pressure growing on the party not to come away empty handed, Biden is stepping up efforts to broker a truce between more conservative members and the left-leaning progressive wing.

At issue are the items on Biden’s original wish list and how to pay for it all. He originally pushed for $3.5 trillion in spending on the social support bill, but the latest figure under consideration is about $2 trillion.

That means axing a lot from the original proposal.

For example, one big item that Biden and his English teacher wife Jill Biden have championed — two years of free higher education at community college — looks set to miss out for now, Biden said. However, he said there was backing for an increase in scholarship money.

But beyond the haggling over where to spend the money is an equally fierce debate over how to pay for the bill.

A keystone of Biden’s pitch has been his call to raise the corporate tax rate, reversing a cut made under his Republican predecessor Donald Trump.

An increase from 21 to 28 percent, along with a hike on taxes for the very richest Americans, would pay for the major spending splurge he sought, Biden says.

Those tax increases, opposed by a minority of Democrats, especially Senator Kyrsten Sinema, now seem unlikely.

“I don’t think we’re going to be able to get the vote,” Biden said.