A transcript published by the White House can be read here.
In his speech, Biden said,
"Congress must restore the right the Supreme Court took away last year and codify Roe v. Wade to protect every woman’s constitutional right to choose.The Vice President and I are doing everything we can to protect access to reproductive health care and safeguard patient privacy. But already, more than a dozen states are enforcing extreme abortion bans.Make no mistake; if Congress passes a national abortion ban, I will veto it."
Dobbs v. Jackson overturned the precedent of Roe v. Wade last year by affirming that the Constitution does not contain a right to abortion. This allowed states to democratically pass and enforce their own laws governing abortion. By passing federal legislation, Biden and other pro-abortion activists hope to override any laws that protect unborn children from abortion.
Biden's statement that he is using his office's power to protect the abortion industry rings true. The Food and Drug Administration has loosened abortion regulations, the Department of Justice is prosecuting pro-life activists, and the Department of Veterans Affairs is using its resources to offer abortion to veterans and their dependents.
Biden's promise to veto any bill prohibiting abortion is designed moreso to feign strength than anything else. It is unlikely that the pro-abortion majority in the US Senate led by majority Leader Chuck Schumer (D-NY) and Majority Whip Richard Durbin (D-IL) would ever send the president legislation banning abortion.