Democrats hoping to resurrect the party’s economic agenda are up against a stumbling block: Sen. Joe Manchin’s desire to raise tax rates clashes with Sen. Kyrsten Sinema’s opposition to doing so.

In a 50-50 Senate, with Republicans unanimously opposed to the effort, the party will have to try to reconcile the pair’s divergent positions in order to secure both votes for a scaled-down version of President Biden’s economic agenda ahead of this year’s midterm elections.

As Democrats’ efforts on the child-care, healthcare, and climate package have stalled in recent weeks, Mr. Manchin (D., W.Va.) has repeatedly stated that an updated version of the bill should focus on increasing government revenue. Raising taxes to more than offset the bill’s spending would reduce the budget deficit and fight inflation, he said, addressing concerns that prompted him to vote against the House-passed bill last year.

Mr. Manchin has proposed raising the corporate tax rate to 25% from 21%, raising the top capital-gains rate to 28% from 23.8 percent, and increasing taxes on carried-interest income for private-equity managers.

However, Democrats abandoned those tax proposals last year due to Ms. Sinema’s opposition (D., Ariz.). The House version of the legislation included alternatives designed to cover the bill’s costs while also addressing her concerns. These policies included a new surtax on households earning at least $10 million per year and a 15% minimum tax on financial-statement income from large corporations.

Ms. Sinema’s spokesman said she would consider proposals that boost the country’s competitiveness and create jobs. Ms. Sinema has expressed concerns about large-scale spending, but, unlike Mr. Manchin, she did not openly oppose specific spending programs during last year’s negotiations.

Other Democrats broadly support the tax increases that Mr. Manchin is once again advocating for, but dropping the proposals was one of many concessions made by the party to Ms. Sinema and Mr. Manchin during months of negotiations last year. Many members of the party were taken aback by the compromise.

Some Democrats have indicated a willingness to meet Mr. Manchin’s demands on which government programs to fund in the bill, even if it means foregoing other goals such as expanding the child tax credit.

Mr. Manchin recently stated his support for tax incentives to reduce carbon emissions and a program to lower the cost of some prescription drugs, while lawmakers and aides believe that funding for universal prekindergarten and healthcare subsidies could be included in an eventual compromise.

Having tax increases exceed spending in the package, so that the legislation reduces the deficit overall, is another way Democrats hope to gain Mr. Manchin’s support. Many tax proposals in the House bill, such as money from tougher Internal Revenue Service enforcement and higher taxes on foreign income earned by U.S. companies, have not sparked much opposition among Democrats.

Last year, the Congressional Budget Office estimated that the roughly $2 trillion House-passed version of the legislation would add roughly $160 billion to the deficit over ten years if the scorekeeper included direct revenue from increased tax enforcement but not the administration’s more optimistic estimates. Mr. Manchin argued that Democrats’ plan to fund some programs temporarily with the goal of extending them later obscured the full extent of the bill’s spending.

Mr. Manchin has argued throughout the months of negotiations against adding to the national debt, which recently surpassed $30 trillion for the first time. Similarly, he has stated that he does not want to pass legislation that would exacerbate inflation, which is at a four-decade high.

Meeting Mr. Manchin’s tax-raising goals may be more difficult for Democrats than cutting some spending, despite the fact that he is proposing far smaller tax increases than Mr. Biden campaigned on. According to people familiar with the remarks, Ms. Sinema repeatedly told donors and lobbyists at events last year that she was opposed to raising the top corporate rate, income and capital-gains rates, as well as higher taxes on carried interest.

Many Democrats share Mr. Manchin’s desire to resurrect the tax-rate increases ruled out by Ms. Sinema, including the corporate tax rate. But after months of grueling negotiations, some lawmakers want the party to focus on established areas with a Sept. 30 deadline for getting the bill through the Senate under expedited rules that let Democrats dodge a filibuster.