In holding a prime-time news conference for the first time in his second term, President Bush had one goal: to counter the growing impression that his Social Security proposals are dead by stressing his efforts to ease the system’s long-term financial problems.

The decision a day later by his faithful House Republican allies to schedule consideration of the issue represents progress, since Senate divisions make agreement there impossible at this time.

But the revised Bush approach still has two potentially fatal flaws.

First, Bush still insists that any plan include the diversion of some Social Security payroll taxes into personal accounts for younger voters. “It’s got to be a part of a comprehensive package,” he said, launching a lengthy defense of the concept he has tried with minimal success to sell in recent weeks.

That firm statement confirmed the view of people on both sides of the issue that his main goal remains creating a private alternative to the Social Security system, something he has favored since his failed U.S. House bid 27 years ago.

But it’s already clear that a majority of the Senate opposes any effort to divert payroll taxes into private accounts. That’s one reason Sen. Charles Grassley, R-Iowa, is having such trouble writing a bill in his Senate Finance Committee.

Second, the specific plan that Bush touted to ease the system’s long-term fiscal problems would fall far more heavily on middle-class Americans than other solutions, which would put the burden mainly on the wealthy.

That could pose a real political problem for lawmakers, even those who favor dealing with Social Security now.

Bush advocated a system in which “benefits for low-income workers will grow faster than benefits for people who are better off.”

Answering a follow-up question, Bush said only 30 percent of Americans would get currently projected benefits. He conceded that “real wealthy people,” as questioner Ron Hutcheson of Knight Ridder put it, would not benefit much from Social Security.

The White House confirmed that Bush was talking about an approach based on Boston investment executive Robert Pozen’s so-called “progressive indexing” plan, which would make up as much as 70 percent of the system’s shortfall in the next 75 years.

But that proposal might be even less acceptable politically than creating a private alternative to the current program because of its impact on the middle class.

Government figures indicate that, under this plan, millions of Americans earning between $36,000 and $90,000 would take a big hit in projected Social Security benefits. Those with higher incomes would lose even more.

But providing for the system’s long-term financial stability by increasing the income level at which the Social Security tax is levied from the current $90,000 would put the burden on a far smaller proportion of Americans since that would only affect some 6 percent of the country’s wage-earners.

There is another way to improve the system’s solvency without placing an additional burden on the middle class. That is to increase the retirement age, now set to go up to 67 by 2027, while keeping early retirement provisions.

Both of those might be more acceptable politically than the Pozen plan. Still, it remains unclear if enough members of Congress share the president’s concern that this is the time to act, especially considering the lack of public support for what he has proposed.

The Democrats seem convinced they are in the right place politically by directing their fire at the president’s private accounts. Republicans, while more inclined to do something, are divided on what to do and nervous about the possibility of a backlash in next year’s congressional elections.

That’s why the decision by Rep. Bill Thomas, R-Calif., chairman of the Ways and Means Committee, to begin hearings on the contentious issue is so important. If Thomas can’t get a majority for some plan in his committee and sell it to the often reflexively pro-administration House, no one can.

In the end, many people here think that Bush would be willing to sign any piece of legislation that he can tout as reforming the Social Security system. But it’s not yet clear if things will get that far in the current political environment.

— Carl P. Leubsdorf is Washington bureau chief of the Dallas Morning News.