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In the District, the exchange will be mostly Internet-based, but services will still be available by phone and other means, city officials said.

Aggressive efforts to cover residents under Medicaid or the D.C. Healthcare Alliance, which enrolls many immigrants who are not eligible for the federal insurance program, means only about 5 percent of the city’s population is uninsured, officials said.

Maryland vs. Virginia

In Maryland, leaders have wholeheartedly embraced the health care law since its passage. The General Assembly passed bills in 2011 and this year that set the framework for a health benefits exchange, which state officials say could provide health care access to as many as half of the state’s 700,000 uninsured residents.

By diving into health care reform, the heavily Democratic state has already received $34.4 million in federal grants and is expecting to receive additional federal funds, avoiding the need for the use of state dollars, according to staff in Annapolis.

Maryland Lt. Gov. Anthony G. Brown, a Democrat and vocal proponent of Mr. Obama’s law, said the state’s health care exchange is “the most important component of our health care reform efforts.”

But further south, the Virginia legislature this year delayed taking action to implement an exchange until the Supreme Court case was resolved. Its Republican state attorney general, Kenneth T. Cuccinelli II, sued the federal government immediately after Mr. Obama signed the overhaul into law and had hoped the entire law would be struck down by the Supreme Court.

In his role as chairman of the Republican Governors Association, Mr. McDonnell sent a letter to the Obama administration in July to outline concerns with the health care law and ask a laundry list of questions, including whether governors can “expect extensions of the deadlines for implementation (of state-based exchanges) given the uncertainty caused by the Supreme Court ruling.”

In a separate letter to the state’s General Assembly, Mr. McDonnell said he hopes to see Mr. Obama’s health care law repealed after the November election if Mr. Obama is defeated in his re-election bid.

Amid this uncertainty, he said, “it is not prudent to spend a great deal of time and taxpayer money on building a system that we may never need to implement or that may be materially different once the rules are finally established.”