NEW YORK (Reuters) - Supporters of billionaire Donald Trump appear unfazed by his decision to accept money from outside donors, despite his earlier vow to self-fund his presidential campaign and his criticism of rivals as puppets of wealthy special interests.

Republican U.S. presidential candidate Donald Trump speaks at a campaign rally in Eugene, Oregon, U.S. on May 6, 2016. REUTERS/Jim Urquhart

The vow has been a cornerstone of Trump’s election strategy to present himself as an outsider who is not in the pocket of rich donors, even though he has accepted more than $12 million in contributions so far. The strategy paid off last week when the New York businessman emerged as the Republican party’s presumptive presidential nominee, after sweeping a series of state nominating contests.

Since then, Trump has said he would no longer self-finance and would work with the party to raise more than $1 billion to help him fight his eventual Democratic Party challenger. Critics accused him of flip flopping, but some supporters don’t agree.

Three dozen of the 40 pro-Trump voters Reuters interviewed said they were not concerned about his reversal. Only four indicated the switch made them uneasy, though all of them said they would still support him.

Most of those interviewed applauded the way the celebrity businessman billed himself as a “blue-collar billionaire” who didn’t need other people’s money, but said they understood Trump would need far more resources to compete in the general election.

They would have no problem donating to the billionaire, albeit in the same kind of small increments that Democratic presidential candidate Bernie Sanders has used to build his nearly $200 million fundraising juggernaut.

“Even though I’m on welfare, I would donate to Trump,” said Pamela Thompson, a 46-year-old mother of three school-age kids from Tulsa, Oklahoma. “And my kids would run a lemonade stand to help elect him.”

The supporters interviewed said Trump’s pledge to self-finance his campaign was less important to them than his promises to crack down on undocumented workers and ease the pain of mostly white, blue collar towns that have seen manufacturing jobs lost to developing countries.

Sharon Jones, a 53-year old Wal-Mart cashier from Coleman County, Alabama, says her anger over undocumented immigrants shopping at her store on welfare benefits is animating her support for Trump, who has promised to deport undocumented workers and build a wall along the U.S. border with Mexico.

“They are doing better than I am on my $9.45 an hour,” Jones said.

The majority of supporters interviewed said they thought Trump’s decision to fundraise was strategically wise given that Hillary Clinton, the front-runner for the Democratic nomination, has raised more than $250 million so far.

In the 2012 election, Republican nominee Mitt Romney and his Democratic opponent, President Barack Obama, each raised $1 billion.

“You gotta fight fire with fire. Bring it on,” said Cheryl Ressler Halvorson, a cattle rancher from Williston, North Dakota whose support for Trump stems mainly from her ire over having to pay $1,100 a month for health insurance with a $13,000 deductible due to the government mandate known as Obamacare.

Halvorson is not an outlier. Most Trump supporters have stayed loyal despite the candidate frequently reversing or updating policy positions on key economic and social issues.

Trump is not the first U.S. presidential candidate to change his mind about financing his election campaign.

In the 2008 election, Obama also did an about-face. He said he would forego public financing of his general election campaign against Republican John McCain. This was a reversal of his earlier stance and it allowed him to pursue a record fund-raising effort. Supporters were unfazed by the shift and Obama went on to win the election.