By David Lawder

WASHINGTON, March 16 (Reuters) - Congressional Republicans will unveil budget proposals on Tuesday that seek to eliminate deficits and nominally stick to spending caps while boosting defense spending by tens of billions of dollars to meet demands within the party.

The spending struggle will unfold for months, culminating in government funding bills needed to start the next fiscal year on Oct. 1. It will be overseen by two rookie Budget Committee chairmen in the Senate and House of Representatives.

Tom Price, the new House Budget Committee chairman, is promising a balanced budget within 10 years that fully repeals "Obamacare" health reforms and cuts social safety net programs by turning them over to states.

The orthopedic surgeon from Georgia is also widely expected to recycle controversial changes to Medicare championed by his predecessor, Paul Ryan, which would turn the popular health care program for seniors into a system of subsidies for private insurance.

On the other side of Capitol Hill, Senate Budget Committee chairman Mike Enzi of Wyoming boasts that he is the first accountant to chair a budget panel. He is expected to echo many of the features of Price's budget in his rollout on Wednesday.

But Enzi is expected to take a more cautious approach, excluding the Ryan Medicare reforms.

The Republicans' budget resolutions will reflect the party's long-standing vision of vanishing deficits, smaller government and lower tax rates that spur job growth.

But both Republican budgets will need to walk a fine line to maintain "sequestration" spending caps and please conservatives, while finding ways to provide more defense spending. Otherwise, they risk failure in both chambers, where moderates and defense hawks argue that years of cutbacks are eroding U.S. military capability when global risks are rising.

A wide-ranging bloc of 70 House Republicans has signed a letter demanding that the budget at least match Obama's $561 billion budget, which ran $38 billion above the caps.

Representative Tom Cole said on Monday that the House budget would add an extra $39 billion to a war funding account that is separate from the caps to boost Pentagon resources. Democrats are certain to deride the maneuver as a "gimmick."

Republican senators have said Enzi intends to propose a revenue-neutral "reserve fund" that will allow for more defense spending under the caps by finding more savings elsewhere. The plan could become a model for an eventual deal to replace the "sequestration" caps they say.

(Reporting by David Lawder; Editing by Kevin Drawbaugh and Cynthia Osterman)