WASHINGTON (AP) — The new House and Senate Republican budgets make a big boast: They both balance the federal budget within 10 years, without raising taxes.

Their own numbers, however, say millions of American families and businesses would have to pay more in taxes to make the math work — about $900 billion more over the next decade.

Both budgets also claim big savings by repealing President Barack Obama's health law. But at the same time, they rely on more than $1 trillion in tax revenue from the health law that would supposedly be repealed.

The House and Senate are scheduled to take up their budget resolutions in the coming days. These are nonbinding political documents that often lack details, especially when it comes to taxes.

Nevertheless, they provide important insight into how majority Republicans in Congress would tackle the federal government's finances.

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THE CLAIM: "First and foremost, we balance the federal budget in less than 10 years by reducing spending by $5.5 trillion — without accounting gimmicks or higher taxes." —Rep. Tom Price, R-Ga., chairman of the House Budget Committee, in a published opinion article.

"Republicans have put forward a responsible plan that balances the budget in 10 years with no new tax hikes, that protects our most vulnerable citizens, it strengthens our national defense, and it improves economic growth and opportunity for hardworking families." —Sen. Mike Enzi, R-Wyo., chairman of the Senate Budget Committee.

THE FACTS: Both Republican budgets say they will generate $41.67 trillion in revenue over the next decade. That is very close to the $41.75 trillion that would be generated under current law, according to the nonpartisan Congressional Budget Office.

However, current law assumes that more than 50 temporary tax breaks that expired at the start of the year will not be renewed. They include tax breaks for businesses big and small, as well as provisions that benefit commuters, teachers and struggling homeowners.

All together, the tax breaks add up to $898 billion over the next decade, according to CBO.

The biggest tax break for businesses is a popular credit for research and development championed by American manufacturers. A big one for families is a deduction for local sales taxes for people who live in states without a state income tax, including Wyoming.

Do congressional Republicans really want to eliminate all these tax breaks?

No. Most Republicans in Congress have voted numerous times to temporarily extend them. And over the past year, the Republican-controlled House has voted to make some of the more popular ones permanent.

Then why don't the Republican budget resolutions reflect the costs of providing those tax breaks?

Balancing the federal budget is hard. Doing it without more tax revenue is even harder.

The House plan would cut spending by $5.5 trillion over the next decade while the Senate plan would cut spending by $5.1 trillion.

Those spending cuts have already raised loud objections from both the right and the left because defense hawks want more money for the military and liberals are concerned about cuts to social programs. Finding the votes for an additional $900 billion in spending cuts would be a tall order.

To explain their numbers, Republican budget writers assert that they can fill the revenue gap by simplifying the tax code and making it more competitive.

Both GOP plans call for overhauling the taxes paid by individuals and businesses. Without providing many details, they count on that overhaul to spark more economic growth, which would generate additional tax revenue.

"Our budget calls for comprehensive tax reform that would include lower rates for individuals and families as well as large corporations and small businesses who often file their tax returns through the individual side of the tax code," says the House plan. "Along with lower rates, we propose broadening the tax base by closing special-interest loopholes that distort economic activity."

The plan doesn't specify which "loopholes" would be closed. That would be left to the tax-writing Ways and Means Committee to figure out later.

The Senate plan creates a reserve fund that could be used to help pay for a tax overhaul or to "extend certain expiring tax-relief provisions." But the budget resolution doesn't allocate any money to the fund.

Some policymakers in Washington say that letting temporary tax cuts expire isn't the same as increasing taxes. But congressional Republicans don't make that argument, especially about tax breaks that have been around for years and even decades.

To drive home the point, when Congress voted in December to extend the temporary tax breaks through the end of the year, the title of the legislation was the "Tax Increase Prevention Act of 2014."

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THE CLAIM: "Our budget fully repeals Obamacare. This will save over $2 trillion, end the Obamacare raid on Medicare and rescind all of the tax increases on job creators and health care innovation." —House GOP budget resolution.

"By adopting this new budget, Republicans can repeal the president's health law and the committees of jurisdiction can continue to work on plans to replace it." —Senate GOP budget resolution.

THE FACTS: In 2012, CBO said repealing the president's health law would reduce tax revenues by $1 trillion over the following decade. That number has certainly gone up as more of the law's tax increases have come into effect.

But despite calling for the health law to be repealed, both budget resolutions include all the revenue that would come from the law's taxes.

House Republicans explain their reasoning on the Budget Committee website, in a question-and-answer section called, "Setting The Record Straight."

"Q: Isn't this budget trying to have it both ways by repealing Obamacare but keeping the revenue from Obamacare's taxes?"

"A: No. The House Republican budget repeals all of Obamacare — including the Obamacare tax hikes while calling for fundamental tax reform. A revamped tax code could raise just as much revenue as the system in place today, but without the harmful tax policies embedded in current law (like the Affordable Care Act)."