Dan Quayle reasserted Monday that he broke no rules nor did anything unfair to get into the Indiana National Guard during the Vietnam War.

Appearing on two television talk shows, Quayle also said he did not think it was hypocritical for him to strongly back the war effort and opt to join the Guard at the same time.And he said he is convinced the furor will die down and can't wait for that to happen. "Right now, I just sit there and answer questions," Quayle said on ABC's "Good Morning America."

Asked about "the question of hypocrisy," Quayle said: "I don't think it's hypocritical. There were a lot of people that were in the National Guard in my National Guard unit that supported the goals of fighting communism in Vietnam but were in the National Guard."

On NBC's "Today" show, Quayle said, "I don't even know what my (draft lottery) number was." Quayle joined the Guard in the summer of 1969. The lottery system of selecting people for the draft took effect Dec. 1 that year.

George Bush, the Republican presidential nominee who selected Quayle to run with him, says he is confident Quayle will surmount the flap over his National Guard duty, but that in the meantime, "I've got to take the heat."

Bush said Sunday that he remains upbeat about his election prospects despite questions about the extent to which family influence helped Quayle avoid being drafted and got him into law school even though he didn't meet admission requirements.

Democratic nominee Michael Dukakis is responding to the controversy by noting that the qualifications of his own vice presidential choice, Sen. Lloyd Bentsen, have not come under attack. Otherwise, Dukakis has kept to his own campaign themes and Monday was visiting northeastern Massachusetts, a region he often cites when discussing his record of economic development.

Bush was speaking to a Veterans of Foreign Wars convention in Chicago then traveling to Seattle later.

Bush was clearly unhappy Sunday with the intense scrutiny of Quayle's background and with Democratic criticism of his own decision-making. He said he's sticking with Quayle, with "no hesitancy," but that the Indiana senator needs time "to get his act together" before campaigning on his own.

Bush, who conducted joint appearances with Quayle in the Midwest over the weekend, said Quayle will begin campaigning alone "as soon as he can get squared away" with a staff and a schedule of appearances.

Quayle stumbled during initial news conferences and interviews after being selected by Bush last week, and Bush aides are spending the early portion of this week trying to prepare him for his first solo campaign appearances, scheduled to begin Wednesday.

Throughout their appearances in Indiana and Ohio, questions continued to be raised about the circumstances of Quayle's enlistment in the Guard at the height of the Vietnam War in 1969. He was 22 then, and described himself at the time as a supporter of the war.

Quayle has said that before his student deferment from the draft expired, he discussed with his family his desire to join the Guard. A former top newspaper employee of the family said he interceded with the Guard on Quayle's behalf.

Questions also are being raised about Quayle's law school admission. The Cleveland Plain Dealer reported Sunday that Quayle did not meet the academic requirements of Indiana University law school but got in anyway after meeting with the admissions dean, a Republican judge in a city where Quayle's family owned the local newspaper.

The Plain Dealer quoted Quayle's father, James C. Quayle, as saying his son met with the dean after being initially rejected by the law school. "He talked his way in," the elder Quayle said.

Bush dismissed questions about the law school admission by saying, "I don't see that there's an enormous demand from the public to learn this guy's high school grades."

Senate Minority Leader Bob Dole, R-Kan., appearing on NBC-TV's "Meet The Press," said Bush campaign chairman James A. Baker III had told him that he believed the military issue was "pretty much behind them." But Dole said his own opinion is that "it's going to last awhile."

Dukakis said over the weekend that people should notice how few have questioned the qualifications of Bentsen to serve as vice president. Other Democrats were quick to challenge Bush's decision-making ability.

"Why did George Bush pick Daniel Quayle? That's got to be the question," House Democratic Whip Tony Coelho, D-Calif., said on CBS-TV's "Face the Nation" program. "His first presidential decision was Dan Quayle. Michael Dukakis' first presidential decision was Lloyd Bentsen."

Dukakis campaign manager Susan Estrich, also on CBS, said that if Quayle is not qualified to be vice president, "at that point, the real issue is not Dan Quayle. It's George Bush and his judgment."

Bush, speaking with reporters on Air Force Two, said no thought had been given to asking Quayle to withdraw, that the 41-year-old senator had not offered to step aside, "and he shouldn't."

"I want him out campaigning," Bush said. "He will have a tremendous appeal to young people, and he'll help with that gender gap.

Bush said he could see nothing wrong with Quayle asking a family member to help him get into the Guard, or college, for that matter.