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Evan Vucci / AP

Sources familiar with the Republican tax negotiations say there's an acknowledgment within the working group that setting the corporate rate at less than 25 percent may be unworkable if the tax reform is going to be revenue neutral.

Why it matters: This is far from the number the administration wants, but a source familiar with the discussions said it's a simple numerical cash problem. They've done away with the border adjustment tax, health care repeal is failing, and there are no politically-palatable alternatives to fill more than $1 trillion in missing revenue.

None of this is to say that Trump has given up on radical tax cuts. He wants the federal corporate rate to move from 35 to 15 percent, and top economic adviser Gary Cohn and Treasury Secretary Steven Mnuchin want cuts of historic proportions. Neither Trump adviser is especially concerned about adding to the deficit in the short-term. The problem is finding the votes for that in Congress.

What we're hearing:

From a source close to Republican leadership: "I don't even know how they get to 25 [percent]! It costs about 110B per point. So, they need to come up with about 1.1T to do a ten point cut."National Economic Council spokeswoman Natalie Strom: "Discussions between the White House and Congress are progressing in a very positive direction. We have always had more areas of agreement than disagreement and we feel confident we will develop a unified plan that will deliver on our goals of economic growth and tax relief for hard-working middle-income families. Decisions are best made through discussions with Members of Congress and staff, not hashed out in the press, and that's exactly what we're doing."A source who recently met with White House tax officials: Their mood as one of "irrational optimism." The source said the reality is they're still having immense problems finding revenues, and figuring out how to eliminate incentives for US companies to park money overseas.A senior administration official believes the impending collapse of health care negotiations will create a sense of urgency among members to ram through tax cuts before the 2018 midterms. He also thought health care's probable failure meant the administration would have a better chance at convincing fiscally cautious Republicans to abandon their demand that tax reform cannot add to deficits.It appears the BAT — a centerpiece of the House GOP tax plan — has had its funeral. An administration official involved in the tax reform effort said there's no point even including it as a topic of conversation.

Go deeper

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Silver medalist Lilly King of Team USA (left) embraces gold medalist Tatjana Schoenmaker of Team South Africa on the podium during the medal ceremony for the Women's 200m breaststroke final on July 30. Photo: Clive Rose/Getty Images

🥇 : U.S. gymnast Suni Lee wins gold in the women's individual all-around

🚣‍♀️: Team USA women's eight rowing fails to reach the podium

🤸🏾‍♀️: Simone Biles reacts to "love and support" after withdrawing from all-around gymnastics and team finals, citing her mental health

🏊: Olympic swimmer Ryan Murphy wins Silver in 200m

📷: In photos: Tokyo Olympics day 6 highlights

🗓: The Olympic events to watch today

🏃‍: Female Olympians push back against double standard in uniforms

Go deeper: Full Axios coverage

Former Michigan Sen. Carl Levin dies at 87

Sen. Carl Levin (D-MI) in 2014. He died Thursday. Photo: Win McNamee/Getty Images

Former U.S. Sen. Carl Levin (D-Mich.) died Thursday, his family and the Levin Center at Wayne Law — which bore his name — confirmed. He was 87.

Why it matters: The Detroit native served for 36 years in the U.S. Senate, serving twice as chairman of the Armed Services Committee and is credited with helping overturn the military's “Don’t Ask, Don’t Tell” rule.

Updated 6 hours ago - Politics & Policy

Military members will be included in Biden's new COVID guidance

Joe Biden. Photo: Anna Moneymaker/Getty Images

Members of the military will be required to get vaccinations or face regular testing, social distancing, mask mandates and restrictions on travel for work, the the Pentagon said on Thursday evening.

Why it matters: The policy was announced for federal workers and onsite contractors earlier on Thursday, part of several new Biden initiatives to get more Americans vaccinated and slow the spread of the Delta variant.