So far as I understand DOMA, it doesn't "protect" man+woman unions quite the way Bush thinks it does. Since marriage has always been defined as an issue of state law, each state has always had the freedom to define marriage how it sees fit, through its legislators or through its judicial system. This is why there are such disparate treatments of the concept of marriage from state to state, manifested in variations of such standards as legal age for marriage, recognition of "common-law" marriage, and recognition of same-gender unions.
DOMA has an interesting history in light of the latter category. In 1993, the Hawaii Supreme Court held that the state must satisfy the highest standard of Constitutional review, "strict scrutiny," to justify restricting marriage to opposite-sex couples. The opinion, published as Baehr v. Lewin, 875 P.2d 225 (Hawaii 1993), characterized the restriction as sex discrimination: persons of one sex are denied the right to marry persons of the same sex, which is a right accorded to persons of the other sex. On remand, the trial court failed to meet the constitutional burden (under which a challenged law will be upheld only if the state can show that the law is necessary to achieve a compelling state interest), and the restriction was found to be unconstitutional.
The import of the Baehr decision was national. Under traditional choice-of-law principles, states recognize as valid a marriage that is valid where contracted unless recognition would violate the state's strong public policy (a doctrine known as "full faith and credit"). The flurry of legislation that followed, including DOMA in 1996 (states are not required to recognize sister state same-sex marriages, and the federal gov't doesn't recognize same-sex marriages) and about 30 state statutes (including CA in 1999, via Prop. 22) declining to recognize same-sex marriages, was largely unnecessary because the Hawaii legislature overruled the Baehr decision in 1997. The quid pro quo was that Hawaii enacted "reciprocal beneficiary" legislation, which extended some marital benefits to two unmarried persons who are ineligible to marry each other.
Other states have taken larger steps towards recognizing same-sex marriage. Connecticut has entered the fray just recently by judicially overturning a similar ban on same-sex marriage. Vermont's "civil union" legislation, enacted in 1999, has the widest scope of recent legislation, under which extends all the state law rights and obligations of marriage to same-sex partners who enter a legally regulated "civil union." California's "domestic partnership" legislation, albeit a more modest step, is unique in that it is not judicially driven legislation as is the case in Hawaii and Vermont and other states. In contrast, Gray Davis' "go-slow moderatism" has established a strong foundation towards the possible future recognition of same-sex marriage on equal par with traditional marriage.
Bush's statement is also confusing because it's unclear how he intends to "protect the sanctity of marriage." The most direct way to do this, of course, would be to pass federal legislation to outlaw same-sex marriage outright ... but there are problems with this. First, as mentioned above, states make marriage laws, not the federal gov't. The federal gov't has already declared that it doesn't recognize same-sex marriage, but it's not clear what else it can do, since people don't get married under federal law (however, there are lots of marital benefits under federal law, such as Social Security, tax concerns, etc.). The federal government can't affirmatively tell the states to refuse to recognize same-sex marriage. Second, if it tries to, it would probably be held unconstitutional on a number of different grounds. For example, there is U.S. Supreme Court precedent (Zablocki v. Redhail, 434 U.S. 374 (1978)) which indicates that a direct restriction on marriage must satisfy strict scrutiny review. Perhaps more importantly, under due process analysis, it is pretty well-settled that marriage is a fundamental right, which, if impaired by a state (or federal) law, receives strict scrutiny review. This standard is rarely met, if ever; one commentator evaluated strict scrutiny review to be "strict in theory, fatal in fact."
Thus, the next best way would be to amend the Constitution so as to get around an unconstitutional rejection. However, U.S. Constitution is unusually difficult to amend. As spelled out in Article V, it can be amended in one of two ways. First, amendment can take place by a vote of two-thirds of both the House of Representatives and the Senate followed by a ratification of three-fourths of the various state legislatures (ratification by thirty-eight states would be required to ratify an amendment today). This first method of amendment is the only one used to date. Second, the Constitution might be amended by a Convention called for this purpose by two-thirds of the state legislatures, if the Convention's proposed amendments are later ratified by three-fourths of the state legislatures.
Because any amendment can be blocked by a mere thirteen states withholding approval (in either of their two houses), amendments don't come easy. In fact, only 27 amendments have been ratified since the Constitution became effective, and ten of those ratifications occurred almost immediately--as the Bill of Rights. The very difficulty of amending the Constitution greatly increases the importance of Supreme Court decisions interpreting the Constitution, because reversal of the Court's decision by amendment is unlikely except in cases when the public's disagreement is intense and close to unanimous. Even unpopular Court decisions (such as the Court's protection of flagburning) are likely to stand unless the Court itself changes its collective mind.
In short, Bush has declared a rather ambitious agenda for himself in terms of shoving some legislation through the works, without much hope of success (IMHO). It's interesting in this respect to note another piece of legislation signed into law by President Bush. The U.S. Federal Victims Compensation Fund, enacted in June 2002 as a response to the events of 9-11, allows same-sex partners of firefighters and policemen killed in the line of duty to receive analogous benefits as spouses of the deceased.