President Bush (search) offered solidarity to tens of thousands of anti-abortion demonstrators Monday, who braved bitter cold to unite in what they call a "generational struggle."

"What unites us is our understanding that the essence of civilization is this: The strong have a duty to protect the weak," Bush could be heard over loudspeakers at the 32nd March for Life.

The day of rallies, a march down Pennsylvania Avenue to the Supreme Court and other activities is organized each year to protest the Supreme Court decision legalizing abortion. Bush, who was not in Washington on Monday, but at the presidential retreat in Camp David, said he is working with Congress to pass "good, solid legislation to protect the vulnerable." He cited his signing of legislation last year to outlaw late-term abortions.

Bush also said that he would continue "seeking common ground where possible and persuading increasing numbers of our fellow citizens of the rightness of our cause. This is the path of the culture of life that we seek for our country."

Members attending this year's event say the tide of public opinion has turned, and the Supreme Court will reverse its 1973 Roe v. Wade ruling and give states the power to establish abortion laws.

"I can stand here in front of you today and say that the end of abortion on demand has started. The end has started," Sen. Sam Brownback, a Kansas Republican, told protesters.

"We have to ask the question: how many more babies, how many more young lives have to suffer this horrible and painful death," said Rep. Scott Garrett, R-N.J.

Also present were women who once had abortions and now have regrets, foremost among them Norma McCorvey, the "Jane Roe" of the Roe v. Wade decision. Last week, McCorvey formally asked the Supreme Court to overturn its decision.

"We look forward to having abortion — the covenant of death — to be overturned," she said.

Abortion foes may find their position is growing in popularity. According to a New York Times/CBS News poll taken in November, 34 percent of those surveyed wanted to keep abortion generally available, as it is now. Forty-four percent wanted stricter limits and 21 percent wanted an outright ban.

But abortion rights supporters say women who seek an abortion rarely have other options.

"Regardless of what people say in the polls, there are very few people in this country who want us to go back to the days of our grandmothers and our great grandmothers, where women had 10, 12, 15, 18 children," said National Organization of Women President Kim Gandy.

Gandy added that current statistics show that abortions are not available in 87 percent of the nation's counties.

"There is an extraordinary effort targeted at abortion providers to try to drive them out of business, and targeted at medical schools to get them to stop teaching new doctors how to perform abortions," she said.

Nineteen states have governors and majorities in both legislatures that oppose current abortion laws. Only three states have governors and majorities in both legislatures that support current abortion law, according to the Naral Pro-Choice America Foundation.

Monday's march, occurring two days after the actual anniversary of the court's decision, comes just as the health of Chief Justice William H. Rehnquist (search) has been called into question. Rehnquist appeared frail at Bush's inauguration last week after undergoing thyroid cancer treatment. Three other justices have had cancer.

One or more court vacancies would give Bush the chance to install another justice or justices who oppose the Roe decision, increasing the likelihood that at some point, the ruling could be overturned.

The Supreme Court also touched a nerve with marchers on Monday, after it let stand a Florida Supreme Court ruling nullifying Terri's law, named after Terri Schiavo (search). That law ordered the use of a feeding tube to keep the brain-damaged Schiavo alive. Her parents are fighting to keep the law intact.

"It's just pathetic what they have done to her — and it's judicial homicide," said Robert Schindler, Schiavo's father.

The high court's decision means Schiavo's estranged husband may soon disconnect her feeding tube. Although the case is unrelated to abortion, many marchers say they see Schiavo's fate as part of a larger struggle to define state control over life.

FOX News' Major Garrett and The Associated Press contributed to this report.