The legislation failed, with a 49-48 vote, to garner the two-thirds majority needed to send the proposed amendment to the states for ratification.
“I thank the senators who supported this amendment, but I am disappointed the Senate did not achieve the necessary number of votes to move the amendment process forward," Bush said in a statement.
Bush said the vote marked "the start of a new chapter in this important national debate."
He suggested that the ban could still be brought through at some future point.
"Our nation's founders set a high bar for amending our constitution - and history has shown us that it can take several tries before an amendment builds the two-thirds support it needs in both houses of Congress," he said.The 49 votes supporting the amendment were one more than the last time the Senate voted on the issue in 2004, despite predictions that the amendment would win at least a 51-vote majority in the Senate with the four Republican seats gained since then.
Supporters of the amendment, however, have come out to insist that progress has still been made despite the defeat. They claim that the profile of the proposed gay marriage ban has been raised over the three days and that this will force candidates to answer to voters over their positions on the issue as they hit the campaign trails.
“Eventually, Congress is going to have to catch up to the wisdom of the American people or the American people will change Congress for the better," said Republican Senator David Vitter of Louisiana.
"We're not going to stop until marriage between a man and a woman is protected," said Republican Senator Sam Brownback of Kansas.
"For thousands of years, marriage -- the union between a man and a woman -- has been recognised as an essential cornerstone of society," he said. "We must continue fighting to ensure the constitution is amended by the will of the people rather than by judicial activism."
The issue will return to the House of Representatives for discussion next month.
