Nothing tests a state’s congressional delegation — its cohesion as well as its influence — like the response to a natural disaster back home.

Just as soon as constituents get safely away from the destruction and beyond their shock, they expect their lawmakers in Washington to deliver aid without limit and without delay.

That will be the test for the two senators and five representatives from Oklahoma — all Republicans — even though President Barack Obama declared this morning that the state “needs to get everything it needs, right away” to recover and rebuild after Monday’s destructive and deadly tornado.

The trouble is this: The delegation is split between budgetary centrists and fiscal hawks, and it’s the latter point of view that dominates.

The most prominent member of the group, Sen. Tom Coburn, is already vowing to insist that any special federal aid in his state be matched with an equivalent amount of cuts elsewhere in the budget. News of his position, first reported by CQ Roll Call’s Jennifer Scholtes, went viral last night on Twitter.

Unless the seven unify quickly behind the alternative — that the Oklahoma twisters are the sort of natural calamity meriting immediate federal assistance without regard to spending caps — the congressional debate over a relief and recovery package will probably bog down quickly.

While it’s the biggest state in the country with an all-GOP delegation, Oklahoma has seen its potential for influence on Capitol Hill slip significantly this year, according to the most recent Roll Call Clout Index. Based on an array of factors —  seniority, positions of legislative power and per capita federal spending among them — Oklahoma’s team is now 38th in power and influence among all the delegations after finishing 33rd in the previous two Congresses. (The state’s 3.8 million people make it 28th in population.)

What this points to, emphatically, is that the Oklahoma lawmakers have a much better chance of leveraging their limited collective power if they speak with one voice about how assistance to their communities should be handled.

The money for Northeast communities crushed by Superstorm Sandy was held up for 13 weeks because of a debate within the GOP over whether the $50 billion should be matched with offsetting cuts.

In the end, it wasn’t offset, in large measure because almost all the Republicans in the relatively powerful New Jersey and New York delegations joined their Democratic colleagues to rebuff the offset campaign by the fiscal hawks.

Both Coburn and Oklahoma’s other senator, James M. Inhofe, voted against the Sandy package after they joined an unsuccessful effort to insist on offsets. They have been relatively consistent in that position toward supplemental spending requests throughout their careers, including voting two years ago against replenishing the Federal Emergency Management Agency’s emergency relief fund when it was about to run dry in the aftermath of an unexpectedly large number of disasters.

Three House members from the state also voted for an across-the-board spending cut to finance the Sandy relief: James Lankford, a member of the GOP leadership team as Policy Committee chairman, and freshmen Jim Bridenstine and Markwayne Mullin.

The two who didn’t were Agriculture Chairman Frank D. Lucas and Tom Cole, who has positioned himself as a bridge-builder between the two budget camps in the caucus — and whose hometown is Moore, where the latest tornado wreaked the most havoc.

Both Inhofe and Lankford appeared on several TV reports this morning, but neither took a clear position on the offset question. Both said it was premature to start talking about legislation because it’s too soon after the deluge to tell how much federal help will be required and also too early to say whether FEMA has adequate reserves to cover the response without an extra appropriation.

The sooner they settle on what they’re asking for, the better for the Sooners.