WASHINGTON – As President Bush struggles with his lowest-ever approval ratings and the national Republican Party reels from two gubernatorial defeats and an increasing sense of unease among voters over its foreign and domestic policy goals, two potential Republican presidential candidates tested themes apparently aimed at distancing themselves not only from their party’s current woes but from the growing Republican pack.

In two speeches that were delivered within an hour of each other on the same city block yesterday, Governor Romney, of Massachusetts, and Senator McCain, of Arizona, drew overflow crowds for messages that focused, in one case, on social issues and, in the other, on a new strategy in Iraq. The speeches seemed to assure that social issues and the war would be persistent themes in two straight presidential elections and, coming on the same day that Senator Clinton delivered a keynote address at the American Bar Association’s annual meeting nearby, that attention here has shifted toward the 2008 presidential race.

Hundreds crowded the Grand Ballroom at the stately Mayflower Hotel for Mr. Romney’s speech at the annual convention of the Federalist Society, a conservative lawyers organization that was founded largely as a counterweight to the liberal American Bar Association. That Mrs. Clinton was addressing the one while Mr. Romney addressed the other reflected a possible effort by both to court core constituencies at the heart of American political life. Mr. McCain gave his Iraq speech at the conservative American Enterprise Institute.

Mr. Romney, who is 58, cast himself as a conservative Republican, touting his ability to be elected governor in what he described as the most liberal state in America. His speech, which bore strong similarities to a speech he gave last week to a group of conservative activists in Iowa, also touched on the terrorist threat and the loss of high skilled jobs overseas.

“You can’t be a tier one military and be a tier-two economy,” he said, to applause. “That’s something Russia tried and obviously couldn’t keep it up forever.”

Mr. Romney has portrayed himself as more socially conservative than he did in previous statewide races as he considers a run for national office. He vetoed a bill in July that would have made emergency contraceptives more widely available and has referred to himself in recent months as “personally pro-life.” During a 1994 run for the Republican nomination against Senator Kennedy, Mr. Romney favored the “safe and legal” abortion language popularized by President Clinton.

“Being a conservative Republican in Massachusetts,” Mr. Romney said, to applause, “is like being a Federalist Society member at an American Bar Association meeting.”

Mr. Romney spent most of his speech yesterday decrying a ruling by the Supreme Judicial Court of Massachusetts last year that legalized marriage in the state. The court did not consider the consequences of its ruling, he said, on the children of gay couples or on the nation as a whole. Sounding the theme of judicial activism, he raised questions about whether other states would have to honor the Massachusetts ruling or whether the children of gay parents “have a right to have a mother and a father.”

“I ask my socially liberal friends,” Mr. Romney said, “Aren’t you troubled by a judiciary that is completely unbound by tradition, precedent, and the law?”

A number of Republican senators are considering a run next year, including Senator Allen of Virginia, Senators Brownback and Hagel, both of Nebraska, Senator Frist of Tennessee, and Senator McCain. Democratic senators who are considering a run include Mrs. Clinton, Senator Kerry, of Massachusetts, and Senator Bayh of Indiana. An October WNBC/Marist College Poll gave Mayor Giuliani and Mr. McCain the best chance of beating Mrs. Clinton in head-to-head races, with both men winning 50% of the vote.

Mr. McCain’s speech featured the sort of plain talk about Iraq that characterized his discussion of domestic issues during his failed 2000 presidential bid. Calling Iraq “a transcending issue” for American foreign policy, he said the stakes there are higher than they were in Vietnam. He said America should increase its troop strength there and redouble its efforts at showing Americans how high are the stakes. He said the American military should do more to exploit divisions within Iraqi society and that the Bush Administration should do more to involve aid agencies in building up Iraqi society.

“Our decisions about troop levels should be tied to the success or failure of our mission in Iraq, not to the number of Iraqi troops trained and equipped,” Mr. McCain said. “And while we seek higher troop levels for Iraq we should at last face facts and increase the standing size of the United States Army.”

Mr. McCain, who is locked in a battle with the White House over legislation he is sponsoring that would prohibit torture and other coercive interrogation tactics, faulted the Bush administration for painting a too rosy picture of Iraq. He said administration officials have repeatedly predicted that success was right around the corner when a more sober appraisal was apt. He said Americans would tolerate increasing troop strength and more casualties if they knew the conflict would end in an independent and stable Iraq.

“The biggest mistake in Vietnam was the lie that the light was at the end of the tunnel, when it turned out to be a train,” Mr. McCain said.

Mr. McCain, who is 69, would be the oldest president ever elected if he won the presidency in 2008. His Web site,www.straightalkamerica.com, notes his appearance at a book-signing November 20 in Columbia, S.C. Mr. McCain’s presidential chances waned because of his poor showing in South Carolina’s early presidential primary in 2000.

Messrs. Allen and Frist were scheduled to attend a fund-raiser in the state earlier this week for a state representative. The state has proved crucial for Republicans in three of the last four presidential elections.