WASHINGTON ( CNN ) -- As thousands gathered Sunday in Washington for a march and rally focused on gay rights issues , lawmakers showed that some of the demonstrators ' key goals face major obstacles ahead . President Obama speaks to a major gay-rights group Saturday night in Washington . Even with President Obama pushing Congress to repeal the Defense of Marriage Act -- a stance he highlighted to one of the nation 's leading gay-rights groups Saturday night , to huge applause -- members of his own party told CNN they 're not in lockstep . `` I 've said in the past I do n't think that 's the way to go , '' Sen. Bob Casey , D-Pennsylvania , told CNN 's John King . He added , `` We can move forward on a lot of measures , but I 'm not sure there 's the support yet for that . '' Sen. Debbie Stabenow , D-Michigan , noted that her state is one of many that has a law prohibiting same-sex marriage . `` So I think , for a number of us , that becomes a challenge , '' she said . Stabenow would not say whether she would vote to repeal the Defense of Marriage Act . The law , signed by President Clinton in 1996 , defines marriage as being between a man and a woman , and ensures that states do not have to recognize same-sex marriages performed in other states . Clinton has since changed his mind , and said he no longer opposes same-sex marriage . Obama does not support same-sex marriage and has said he believes marriage is between a man and a woman . He does , however , support civil unions for same-sex couples that offer similar rights and protections . The two Democratic senators on Sunday expressed support for the president 's stances on several other key issues regarding gay rights , including legislation expanding the definition of hate crimes to include attacks based on sexual orientation and gender identity . The bill passed the House last week . Both also expressed support for the president 's efforts to end the military 's `` Do n't ask , do n't tell '' policy . On NBC 's `` Meet the Press , '' Sen. Carl Levin , D-Michigan , said he thinks the president will succeed on that front . `` I think he will and he can , but it has to be done in the right way , which is to get a buy-in from the military , which I think is now possible , '' Levin said . `` Other militaries in the West -- the British and other Western armies -- have ended this discriminatory policy . We can do it successfully , but it ought to be done with thoughtfulness , with care and with a buy-in from the military . '' Retired Gen. Richard Myers , former chairman of the Joint Chiefs of Staff , said , `` Gays can serve in the military ; they just ca n't do so openly . And they do , and there are lots of them , and we 're the beneficiary of all that . '' Myers did not weigh in on whether the change should happen , but said he agreed with Levin that the `` senior military leadership needs to be part of this , the Pentagon needs to be part of this . '' But retired Army Gen. Barry McCaffrey disagreed . `` There 's no question that it 's time to change the policy . The key to it is n't buy-in from the military ; it 's for Congress to change the law . They ought to do so , and I 'm confident that the military will move ahead on it , '' he said . Sen. Lindsey Graham , R-South Carolina , rejected McCaffrey 's suggestion . `` It 's my belief that if you do n't have buy-in from the military , that 's a disservice to the people in the military . They should be included in this . I 'm open-minded to what the military may suggest , but I can tell you I 'm not going to make policy based on a campaign rally , '' Graham told NBC . `` If this policy about 'Do n't ask , do n't tell ' changes , it should be done based not on politics , but on reason . '' In his speech Saturday night to the Human Rights Campaign -- the nation 's largest gay rights group -- Obama praised the gay community for making strides in equal rights and pledged to deliver on major campaign promises that critics say he 's left on the back burner . `` For nearly 30 years , you 've advocated for those without a voice , '' Obama said . `` Despite the progress we 've made , there are still laws to change and hearts to open . ''
Some Democrats cautious about Obama 's pledge to end Defense of Marriage Act . Some say they think he 'll succeed in ending military 's `` Do n't ask , do n't tell '' policy . Others debate whether military `` buy-in '' is necessary to end that policy . Thousands of gay and lesbian rights supporters hold rally in Washington on Sunday .