President Barack Obama says the federal government has a central role in helping the public. Republican believers in limited government generally disagree.

Yet on a variety of policy fronts, pressing financial and other needs are forcing some Republican leaders to concede that minimizing Washington isn’t necessarily a one-size-fits-all solution.

Natural disasters batter states, and offers of federal dollars for health coverage are tough to reject.

This past week saw the president tour the New Jersey shore tour with GOP Gov. Chris Christie. Though a fiscal conservative who has shown no patience for massive government spending, Christie has fought to win billions of dollars in federal aid for his state after Superstorm Sandy.

When Congress stalled on storm aid, it was Christie and other Northeast Republicans who criticized members of their own party for insisting that the spending be offset by cuts elsewhere in the federal budget — a stipulation resisted by the Democratic-majority Senate.

“Republicans, Democrats, independents — we all came together, because New Jersey is more important and our citizens are more important than any kind of politics at all,” Christie said Tuesday.

Two days earlier, it was Oklahoma Gov. Mary Fallin, another Republican with a distaste for over-the-top government spending, who welcomed Obama and the post-tornado aid his administration brought.

In Arizona, GOP Gov. Jan Brewer, though no friend of the president, is in a fight to force lawmakers in her conservative-leaning state to embrace a dramatic expansion of Medicaid made possible by an infusion of federal dollars under Obama’s health care law.

Although she joined other Republican governors in suing the Obama administration over the law, she is now telling the Republican-controlled Legislature that she will veto every bill sent to her until lawmakers approve the expansion.

Rejecting the Medicaid dollars under the new law, with Washington offering to pay 100 percent of the cost for the first three years, would mean telling about 300,000 low-income Arizonans they’re out of luck while their counterparts in other states get coverage.

“I never liked the Affordable (Care) Act,” Brewer said this year. “But we don’t cut off our nose to spite our face.”

She joined eight other Republican governors, including Christie, in calling for the expansion to go forward. Six of those governors have received legislative approval or appear on track to do so.

“I think governors who take that are being expedient,” said Chris Chocola, the president of the fiscal conservative group Club for Growth. “They’re certainly not limiting the size of government.”

White House officials claim it’s consistent with what they see as a Republican pattern of railing against the government until something happens in their state or district that merits assistance or rescue.

“Instead of not in my backyard, the GOP philosophy is only in my backyard, not anyone else’s,” said Dan Pfeiffer, a senior White House adviser.

Republicans say the differences among them are generally small and their overarching philosophy remains intact. On disaster aid, for instance, they say Republicans have consistently supported it as a concept; the key question is how to pay for it.

“The conservative movement and the Republican Party is not arguing for a government the size of zero. It’s arguing for a government that acts responsibly and makes decisions about priorities,” said Dan Hazelwood, a Republican strategist whose clients have included President George W. Bush.

He contrasted that to the position of Democrats, who he said “want to just increase everything.”