It's official. Republicans are pressing forward to overhaul the tax code after their bruising failure to repeal and replace Obamacare. On Thursday, House and Senate leadership said they want to have a tax bill written in the fall. And House Republicans have released a budget plan that sets the basic framework for it.

The budget plan focuses on what Trump and Republicans have repeatedly said they want: lower corporate and businesses taxes, no alternative minimum tax, lower rates for individuals and a territorial tax system, which basically mean taxing businesses on their US income, not money earned abroad. (And as we've reported before, their plan will overwhelmingly benefit the richest Americans.) The border-adjustment tax — which would have helped pay for all these tax cuts — is now dead.

Yet the fate of tax reform seems more uncertain now than ever. Failing, so far, to repeal Obamacare means Republicans have less money to work with in their drive to cut taxes. Fractures within the Republican Party have grown more glaring. And while pivoting to tax reform suggests that Republicans will have a fresh start, the baggage they bring with them makes the chance of rewriting the tax code just as hard — or even harder — than agreeing on a health care plan.

On taxes, Republicans seem to have a common goal: cut taxes to, they argue, boost the economy. But finding agreement on how to rewrite the tax code was nearly impossible even with a more unified Republican Party in the Reagan years.

Plus, on health care, they seemed to share a common vision too: repeal the Affordable Care Act and replace it with something else, which would presumably cost consumers and the government less. If there is one thing the health care fight revealed, it's that Republican lawmakers have wildly different views on how to achieve their goals.

The death of the Senate's health care bills on Friday shows that Republicans have very little wiggle room, says Scott Greenberg, a senior analyst at the conservative Tax Foundation.

"In the Senate, the margin for defection is so small," he said. "In the House, you can lose many [Republican] representatives and still pass a bill. But you're toast if you lose three in the Senate."

The Obamacare taxes are still here

The most direct impact from the failure to pass a repeal bill is that it leaves about $800 billion in Obamacare taxes in place. That includes taxes on insurers and medical device makers, a 3.8 percent tax on investment income and a 0.9 percent payroll tax on high-income earners. These taxes helped pay for the expansion of Medicaid and federal health insurance subsidies.

Republican lawmakers have long wanted these taxes gone, and the special interests they represent are now going to lobby hard for Congress to eliminate them through the tax overhaul. If Republicans do end up cutting those taxes, they need to find an extra $800 billion or so to offset the lost revenue.

"That’s going to be far tougher, it may be a bridge too far," said economist Doug Holtz-Eakin, executive director of the conservative American Action Forum.

It's especially hard because Republicans plan to use the same reconciliation process to pass tax reform that they used with health care. The process allows Congress bypass a Democratic filibuster and pass a bill with a simple majority. But the process invokes some strict rules, such as prohibiting a bill from adding to the federal deficit beyond 10 years.

Another lesson from the Senate's health care bill fiasco: Not all Senate Republicans want to repeal all the Obamacare taxes. The last version of the BCRA left two taxes in place —the one on investment income and high earners — to appease moderates who were worried about cutting taxes on the wealthy at the expense of low-income Americans who would no longer be able to afford health insurance.

“The challenge is, if we do things, we also have to find a way to pay for it,” Sen. Mike Rounds (R-SD) told reporters last month. “I think we ought to take a look at the investment tax that’s in the system and whether or not it would be appropriate to allow that tax to remain so that we can afford to pay for some of these additional costs.”

So while Republicans are generally in favor of cutting taxes, it's very possible that moderate Republicans will hesitate to endorse a tax reform bill skewed so heavily to cutting taxes for the wealthy.

That won't fly with voters either, said Chuck Marr, director of tax policy for the left-leaning Center on Budget and Policy Priorities.

"The Republican tax-reform plan is basically to cut taxes for hedge funds and people will see that," said Marr. "As we saw with [the health care bill], that won't be something popular to vote on."

Who will pay for tax cuts?

The deep division that surfaced between conservative and moderate Republicans in the health care fight will play out in a different way in tax reform. It will mainly involve disputes about how to pay for the trillions of dollars in tax cuts House Republicans and the Trump administration want.

Someone is going to have to pay. Under the strict reconciliation rules, the tax bill cannot add to the deficit, so Congress can't just cut trillions of dollars in taxes and then borrow money when it can't pay its bills. And so far, Republicans don't seem to agree on how to offset the cost of tax reform.

The House's budget plan does give a clue about what House Republicans are thinking. The instructions in the budget say that the bill has to be "deficit-neutral" but says nothing about being revenue neutral. A deficit-neutral plan leaves open the option to offset part of their tax cuts by cutting spending on government programs.

The budget instructs House committees to cut at least $203 billion over 10 years from programs they oversee, which could include Medicare, Medicaid, and food stamps. This is clearly what the conservative Freedom Caucus wing of the House is pushing.

But that's a sharp contrast from what Senate Majority Mitch McConnell wants to see. In May, he told Bloomberg News that tax reform has to be revenue neutral. That means that Republicans can't cut spending to pay for tax cuts. Instead, they would need to broaden the tax base, which means eliminating a lot of tax breaks, credits and deductions that Americans and businesses love. That could include popular tax deductions, like the ones taxpayers can claim on payments for mortgage interest, student loans and local taxes. (Remember the uproar that led Trump to clarify that he didn't want to remove the deduction for contributions to 401(k) retirement accounts?)

As many tax policy experts like to say, every tax break and every deduction has a constituency, and the people and businesses who get them will lobby hard to keep them.

Meanwhile, the White House doesn't have a clear stance on how to pay for the massive tax cuts either. The administration has resisted choosing who will lose special tax breaks and deductions to offset the tax cuts, instead relying on optimistic forecasts of additional economic growth. Treasury Secretary Steve Mnuchin and White House Budget Director Mick Mulvaney have repeatedly suggested that tax cuts will spur enough economic growth to pay for all — or most — of the tax cuts. (Most economists do not believe that growth alone can carry that entire burden.)

Mulvaney is counting on the economy to grow by at least 3 percent a year. Meanwhile, analysts at the Congressional Budget Office don't think it’ll grow more than 1.9 percent.

To make matters more confusing, Trump at one point said it was okay if tax cuts added to the deficit. That contradicts what congressional Republicans — and his own staff — have been pushing. It means Republicans could not use the reconciliation process, which means they would need Democratic votes to pass a bill.

So far, the White House has not shown the kind of leadership needed to pull off the enormous task of overhauling the tax code.

Holtz-Eakin, of the American Action Forum, points out how hard it was for President Ronald Reagan to rewrite the tax code 30 years ago. "He wrote the bill and it still died twice before it got passed," Holtz-Eakin said. "This will only get done if the White House is effective and all."

And Trump’s track record on repealing Obamacare so far suggests that this is far from a given. He may be about to find out, as he did with health care and North Korea, that tax reform is yet another issue that’s much harder than he thinks.