* Obama makes more calls to Republican senators
* Republicans announce plan to prevent government shutdown
* Measure seeks to extend funding for agencies to Sept. 30
* Pentagon would get more flexibility than domestic agencies
By David Lawder and Richard Cowan
WASHINGTON, March 4 (Reuters) - Tension over the U.S. fiscal crisis eased on Monday as President Barack Obama called more opposition lawmakers to find a way to stop $85 billion in damaging budget cuts and congressional Republicans announced a plan to prevent a government shutdown.
Eager to resolve fiscal fights overshadowing his second term, the Democratic president called Maine Republican Senator Susan Collins and Oklahoma Republican Senator Tom Coburn after speaking to other Republican senators over the weekend.
An aide to Collins, a moderate, told Reuters that the pair discussed the need for a bipartisan agreement on critical issues such as reining in the $16.7 trillion federal debt and dealing with the cuts, also known as sequestration.
In telephone calls over the weekend, Obama raised the issue of cutting entitlement programs, which include Medicare, the healthcare program for the elderly and disabled, and Social Security retirement benefits.
"I will continue to seek out partners on the other side of the aisle so that we can create the kind of balanced approach of spending cuts, revenues, entitlement reform that everybody knows is the right way to do things," he said at the start of a Cabinet meeting on Monday.
After bruising encounters in recent months, Republicans and Democrats in Congress appear to have lost some of their appetite - at least temporarily - for more confrontation over the budget.
Republicans in the House of Representatives turned their attention to avoiding a crisis around the next fiscal deadline: the March 27 expiration of funding for government agencies and programs.
Should Congress fail to pass a new spending measure, the government will have to shut down most agencies and services - from national parks to the Federal Aviation Administration.
That would pile even more uncertainty onto the economy just as Americans start to feel the full effects of the sequester cuts.
RELIEF FOR PENTAGON?
A Republican bill announced on Monday would give some relief to the Defense Department, the Veterans Administration and military construction.
But Democrats complained that it does not do enough to help domestic programs also hit by the sequester cuts.
Introduced by House Appropriations Committee Chairman Hal Rogers, the measure would prevent a government shutdown by extending funding through the end of the fiscal year on Sept. 30.
But the automatic spending cuts would stay in place, drawing criticism from Democrats that it only addresses a small part of Washington's budget woes.
The fiscal crisis that has been going for months took its most serious turn yet when the automatic spending cuts came into force on Friday night because the two parties could not agree on an alternative.
Hundreds of thousands of federal government employees face furloughs, although many will not begin until early next month.
But Secretary of Homeland Security Janet Napolitano on Monday advised airline passengers to get to airports early because the cuts already have led to long lines at some security checkpoints.
Napolitano said delays were up between 150 percent and 200 percent at certain airports.
The Customs and Border Protection agency began reducing overtime over the weekend.
"Lanes that would have previously been open due to overtime staffing were closed, further exacerbating wait times at airports with typically longer international arrival processes," the agency said.
In Chicago O'Hare International Airport, Dave Wagner, 51, of Boston, and his brother John, 48, of Chicago, arrived Monday morning on a flight from Hong Kong.
It took them an hour to clear customs and the wait appeared to be growing. "It should have taken maybe 15 or 20 minutes," said Dave Wagner. "But there was only one agent for 12 lines."
Sequestration has hit the Pentagon the hardest. The House Republican bill gives it some respite by allowing it to shift funds from outdated, unwanted projects to critical, front-line activities.
"The legislation will avoid a government shutdown on March 27th, prioritize DoD and Veterans programs, and allow the Pentagon some leeway to do its best with the funding it has," Rogers said in a statement.
The Pentagon would be allowed to spend about $10 billion more on operations and maintenance than under a straight extension of previous funding that keeps money locked in unwanted accounts.
This would help it maintain training and readiness and provide Republicans a way to shield the military from some of the cuts.
But domestic programs, such as education funding and transportation security would be stuck with outdated extensions of spending authority passed 15 to 18 months ago, limiting their ability to shift funds.
Accounting for the sequester cuts, the Republican bill would reduce the government's full-year discretionary spending levels to $982 billion, compared to $1.043 trillion previously.
The Republicans' measure also steers some new funds to certain security efforts without increasing the overall spending cap.
These include nuclear weapons modernization, FBI staffing levels and cybersecurity programs, border protection and federal prisons. It would also provide another $2 billion above the current level for embassy security after last year's attacks on a U.S. diplomatic mission in Benghazi, Libya.