By David Morgan, Bo Erickson and Davide Barbuscia

WASHINGTON (Reuters) -As President Donald Trump's Republicans push ahead on a sweeping tax-cut and spending bill that nonpartisan analysts say could add $3.3 trillion to the nation's debt over the next decade, they're taking a new approach - denying there is anything to worry about.

Instead, they argue that extending and adding to tax cuts signed into law by Trump in 2017 during his first term - which were set to sunset in 2025 to limit their hit to the deficit - will not drive the debt higher.

Independent analysts and investors said the approach, which follows years of growing government debt under both parties, threatens to erode the country's fiscal health and further sap confidence in financial markets, already shaken by Moody's move in May to strip the U.S. of its top-tier AAA rating.

The bill, passed by the Senate on Tuesday and which House of Representatives Republican leaders aim to pass later this week, will also raise the federal government's self-imposed debt ceiling by $5 trillion, averting the risk of a disastrous default on the nation's $36.2 trillion in debt sometime this summer.

A handful of Republican deficit hawks have said that fact alone undercuts their party's argument that the bill does not add to the debt.

"They are effectively moving the goal posts and making it much easier to run these incredible deficits ad infinitum," said Robert Tipp, chief investment strategist and head of global bonds at PGIM Fixed Income, which manages bond funds worth around $860 billion as of March. "That should really create concern in the market about these ongoing large budget deficits."

Democrats - effectively sidelined by a Republican maneuver that bypasses normal chamber rules requiring 60 of the 100 senators to agree on most legislation - have blasted the Republican argument as chicanery.

They say the bill, which would also lift taxes on tips and overtime, and boost spending on the military and border security while cutting spending on Medicaid and food assistance, will disproportionately help the wealthy and burden lower-income Americans.

"It is fakery. The budget numbers are a fraud, but the deficits will be very real. The prospect of a catastrophic debt spiral is very real," Senator Ron Wyden of Oregon said on the Senate floor on Monday.

Republican Senate Finance Committee Chairman Mike Crapo argued that extending the 2017 tax cuts will not add to the debt.

"If you don't raise taxes, you're not changing the tax code, you're making it bring in the same revenue that it brought in before," said Crapo, of Idaho. "You're not increasing the deficit, you're protecting their wallets."