The phrase "significant outrage" is correct and usable in written English.
It can be used to describe a strong and notable reaction of anger or indignation towards a particular issue or event.
Example: "The government's decision to cut funding for education sparked significant outrage among parents and teachers."
Alternatives: "considerable anger" or "major indignation."
There is significant outrage on Capitol Hill that the $250 billion slice of the program that has gone to recapitalize the banks might not be enough.
After sparking significant outrage, Limbaugh issued a rare, public apology.
Nor did Conservatives try to drum up significant outrage to inspire their conservative base.
There was also significant outrage when it became public that the now discredited science journalist Jonah Lehrer was paid $20,000 to speak at the Knight Foundation about plagiarism and other forms of journalistic misconduct that he has engaged in.
In recent days the White House, partly in response to polls showing the significant public outrage over high fees charged by credit card companies, has begun to work for its passage.
In previous years, attacks during the final days of Ramadan, when Afghans flock to markets for sweets and new clothes, or during the Eid festivities have stirred significant public outrage.
Yet, I think this was also a significant year of outrage and a turning point for women's rights.
Because of the adverse environmental impact, public outrage and significant financial losses, the integrity of the pipelines is essential.
Two months of international outrage and significant pressure later and the authorities have announced the arrest of four suspects — two of whom are employed by the company building the massive dam she had dedicated her life to fighting, and three of whom are former soldiers.
It also pushes significant events through the daily outrage cycle very quickly.
Studies have shown that state control over media can often divert outrage onto less significant or less deserving targets.
