The U.S. has staged a rapid retreat from plans to speed up the green-card application process in a way that would have helped Indian H-1B visa holders, but that doesn’t mean President Barack Obama’s attempt to modernize the U.S. immigration system has been derailed, immigration experts say.

The State Department on Sept. 9 ramped up the number of people that would be allowed to apply for green cards this month, triggering a rush by thousands of people from India, China, Mexico and the Philippines that had been waiting years for their turn to apply. Many of potential applicants readied their paperwork—which requires health certificates, and documents such as birth and marriage certificates that sometimes need to be translated into English—only to be told on Sept. 25 that they would not be allowed to apply yet.

“Words cannot express how frustrated I am with the Department of Homeland Security and the Department of State,” said Brent Renison, a Portland-based immigration attorney in his blog on visa issues. “Families, not just hundreds but thousands of families, who had hopes to apply for a green card in October, and who have worked diligently over the past weeks to collect documents, get medical exams, pay immigration lawyers like me, are suddenly with only a few days’ notice having their hopes and dreams dashed by what appears to be a government mix-up.”

There is now a class-action suit that challenges the decision by the government saying that several applicants spent thousands of dollars on medical tests, gathering and translating documents and retaining lawyers only to find out later they were no longer eligible.

While the people who were ready to apply this month are upset by the mistake–which some are calling “visagate”—it doesn’t mean that the immigration reform Mr. Obama is trying to implement through executive order is dead.

The intention of the measure announced in early September was to allow people to apply for green cards earlier and that is happening, experts say, but not as fast as first announced. In recent decades the wait for a green card has gone from months to decades sometimes depending on the type of applicant as this visual exploration of more than 20 years of State Department data shows.

Being allowed to apply for a green card is important because having a pending application gives migrants more freedom. An H-1B visa holder, for example, has to ask for permission to change jobs. A person with a pending green card application can more easily obtain special permission to switch to a better job. Those with a pending application can also have their children accepted under their green card even if the children become adults while they wait for final approval.

Under the new system announced in September—which uses two different dates to set the waiting list that decides who gets to apply for a green card—Indians holding H-1B visas may be able to apply up to six months earlier than under the previous system, according to Michael Wildes, managing partner at Wildes & Weinberg, a New York-based immigration law firm.

“This is part of the streamlining that President Obama promised,” Mr. Wildes said.