Ms. Sinema, a key vote in the evenly divided Senate, has made clear she won’t support the package’s current $3.5 trillion price tag, announcing her opposition in July and reiterating it since then. The first-term senator from a swing state has held meetings with party leaders to discuss the legislation, but she hasn’t publicly suggested specific changes. Many Democrats remain uncertain over her policy stance and her political calculations…

Six of those conversations were with President Biden directly and three were with Senate Majority Leader Chuck Schumer (D., N.Y.). The rest were with Sen. Mark Warner (D., Va.), who is a member of the Finance and Budget committees, and White House and Democratic leadership staff. Representatives for Messrs. Biden, Schumer and Warner didn’t respond to requests for comment…

In private negotiations, Ms. Sinema has been focused on targeting how the funding of new programs will be distributed among income levels, according to Senate Democratic aides. Narrower targeting of benefits could lower the overall cost. Ms. Sinema has also expressed concerns centering on the structure of the proposed tax changes, aides said.

In a recent interview with the Arizona Republic, Ms. Sinema expressed interest in climate proposals, which she said would directly affect the desert state which is already experiencing droughts, wildfires and damaged infrastructure.