Support is mounting for an online petition that would force the White House to take a hard look at a proposal cutting back on Basic Allowance for Housing for dual-military couples and for troops who share housing with other service members.

The petition, created May 29, has already gathered more than 36,000 signatures on the way to reaching its goal of 100,000 within one month, according to the whitehouse.gov website.

The petition targets the proposal floated by the Republican-controlled Senate that would limit dual-military couples to one BAH payment, specifically one equal to the rate due to the couple's higher-ranking or senior-most service member.

The proposal also would reduce BAH payments for many unmarried troops who share a home or apartment with another service member. For those in paygrades E-4 and higher, they would see their normal BAH rate cut back by 25 percent.

About 40,000 dual-military couples are on active duty around the world today, according to the Defense Department.

Troops' BAH has become a target for cutbacks as the Pentagon faces budget caps and their enforcement mechanism known as sequestration.

Last year the Defense Department officially urged Congress to cut today's housing benefit to one that would cover only 95 percent of estimated housing costs. Congress gave that a cool reception last year and approved only a 1-percentage-point reduction, to 99 percent.

The proposal in this year's Senate defense authorization bill would impose further gradual reductions.

The outcome of those proposals remains unclear. The House version of the annual defense bill does not contain any changes to BAH.

If the petition gathers 100,000 signatures, the White House promises to review the matter and provide an official response. But the real impact of that might be moot, since Obama has already voiced strong opposition to the Republican proposal.

The Obama administration said the targeted cuts to BAH would "impose a marriage penalty," and "have a disproportionate negative impact on women service members," according to a June 3 statement outlining the administration's views on the Senate version of the 2016 defense authorization bill.

The cuts targeting families "will degrade the culture and environment needed to keep our military open and welcoming to military families and risks sacrificing the strengths they bring to our nation's defense," the Obama administration's statement said.