Heads of the departments of Veterans Affairs, Housing and Urban Development, and Labor on Monday backed off the White House's stated goal of ending veterans homelessness by the start of 2016, instead emphasizing "sustainable" plans to permanently end the problem as soon as possible.

"I think all of us are fixated on getting to the goal eventually and not whether it's Dec. 31 or Jan. 1," said VA Secretary Bob McDonald. "We want to build a system that is sustainable because we know there will be variation over time."

The three Cabinet officials joined Interagency Council on Homelessness Executive Director Matthew Doherty in Houston for the start of a three-city tour to highlight partner efforts to get veterans off the streets — a goal outlined by White House officials five years ago.

Since then, the number of homeless veterans has been reduced by more than 25,000 individuals, but between 40,000 and 50,000 veterans are believed to still be struggling with homelessness.

Advocates have acknowledged that reaching the goal of getting all of those veterans into housing by year's end — the White House's original goal — will be difficult.

Monday's event in Houston was designed as a celebration of advances that city officials have made to reduce their homeless veterans population and of systems already in place that officials say over time will find housing for every troubled veteran in their city.

Already, officials in New Orleans, Salt Lake City and Phoenix have announced they've hit "functional zero" on their homeless veteran population. But Houston, with the fourth largest metropolitan population in the country, would be the largest city so far to solve the problem of how to help those veterans.

The functional zero designation doesn't mean veterans in an area won't ever become homeless, but instead means city services have enough beds to quickly shelter homeless veterans and systems in place for effective outreach to them.

"If Houston can do this, it means that any other big city can do this," said HUD Secretary Julian Castro. "We're going to reach that goal."

Whether officials can reach the goal of zero homeless veterans by the end of 2015 won't be known until well into 2016.

Officials use the annual federal point-in-time count each January as a marker for the effort, and that data typically isn't finalized until the fall. That means that despite the deadline in seven months, the estimate of homeless veterans at the start of 2016 won't be available for about another 15 months.

The original version of this story contained an inaccurate quote attributed to VA Secretary Bob McDonald. The quote has been corrected.