AUSTIN, Tex. — Hundreds of activists and uninsured Texans plan to rally at the steps of the Capitol here Tuesday, increasing the pressure on Gov. Rick Perry and other Republican leaders to switch their stance on expanding Medicaid, a major provision of President Obama’s health care overhaul.

Mr. Perry has told federal officials that Texas has no intention of expanding Medicaid, the government health insurance program for low-income and sick people, saying he would not take part in socializing health care and admitting millions of Texans into an unsustainable program at a cost of billions to taxpayers. When Mr. Perry made his decision official in July, he wrote of standing “with the growing chorus of governors who reject the Obamacare power grab.”

In recent weeks, however, that chorus has diminished, as several Republican governors who had resisted the expansion — including Chris Christie of New Jersey and Rick Scott of Florida — said they would accept federal money to expand the program. Meanwhile, the number of state organizations and individuals who vocally support an expansion in Texas has grown.

Several cities and counties have passed resolutions calling for expansion of the program — including the City Councils of Austin and Waco — as have health care and financial experts, including Elena Marks, former director of health policy for the City of Houston, and Ray Perryman, an influential economist in Waco. The Texas Medical Association, which represents more than 47,000 physicians and medical students, asked state leaders to expand the program while instituting reforms. The Chambers of Commerce in Dallas, Fort Worth, San Antonio and other cities also support expansion.