At 10 a.m. Tuesday, Rep. Bob Traxler, a Michigan Democrat committed to vote against the administration's tax-cut bill, got a call from President Reagan. No, Traxler told the president in a cordial conversation, he wouldn't change his vote.

At 1:30 p.m., a presidential aide tried again. Still no.

Twenty minutes later, the long-distance calls started humming into Traxler's office. A top executive of General Motors, another from Dow Chemical, a vice president of Ford, finally a lobbyist began casually, "no big deal, but . . . ."

Traxler stood his ground, but others didn't. And that, at least in part, is how Reagan conquered the House yesterday.

There was more than just skillful stroking. As occurred last month when the House narrowly adopted Reagan's proposed spending cuts, there were deals, or at least reports of them.

Rep. Glenn English (D-Okla.), for example, was invited up to see Reagan at Camp David over the weekend and then got a note from the president Monday. Reagan's note promised that he would veto "with pleasure" any bill that might put a windfall profits tax on natural gas -- a concern in English's district.

English, until yesterday uncommitted on the tax cut bill, voted with Reagan.

Rep. Mario Biaggi (D-NY.) issued a press release expalining he would vote for the president's tax bill because of a Reagan commitment to support restoration of the Social Security minimum benefit. That commitment, which turned out to be qualified, came in a call from Reagan yesterday morning, Biaggi said.

There were rumors, not confirmed, that the Georgia delegation had changed from opposition to support of the Reagan plan because of peanuts. The rumor was that the White House had agreed to soften its stance on a phase-out of farm supports for peanuts, an important Georgia commodity. Georgia voted eight to two for Reagan yesterday.

Deal or not, there was no question that the peanut-minded Georgians were trying. Ten days ago, at a White House meeting with Reagan, a southern legislator raised the issue.

Rep. Dan Glickman (D-Kan.), who was at the meeting, recalled it. "I was so embarrassed. But Reagan handled it very well. He said he didn't know about peanuts. He wanted to talk about taxes."

Glickman, another of the uncommitteds right up to the final vote, was romanced for a full week. He said he had many calls from the White House, two from Reagan himself. The secretaries of agriculture, energy and the treasury called.

"There was no hard sell or threats," Glickman said, "and I told the White House liaison that if they tried to pressure me I would go the other way."

No pressure, no hard sell. Glickman voted with Reagan.

Glickman was among the many House members reporting telephone calls that numbered in the thousands, apparently generated by Reagan's televised speech Monday, as well as other stimuli.

A radio station in Michigan was broadcasting Traxler's office phone number and for two days his lines were jammed, mostly by people urging him to support Reagan.

If Traxler didn't bend, others did. Rep. Dave McCurdy, a bright freshman Democrat from Oklahoma, was invited to Camp David and bombarded with calls from his district. Reagan phones him yesterday.

There was reason for concern about McCurdy. He had stuck with his party on previous key budget votes. He thinks he should be loyal to his party, but he wants to move it "more to the mainstream."

Dave McCurdy succumbed, and now he expects something in return.

"It's accessibility," he said. "You like to know you have access an I feel I have it more so now. The president said he would remember . . . . I have three military bases in my district. I just want to know that if we come to a crunch over that, they're going to remember me."

And that's the way it was all around the House. Wherever one looked, the Reagan blitz had struck -- personal calls, White House follow-up, grass roots voters, power brokers and personal friends phoning from the home districts, employes calling because their bosses told them to. Reagan himself called 18 congressmen yesterday.

Rep. Charles Wilson (D-Tex.) said he was flooded with calls from his huge, rural district in east Texas. Wilson voted with Reagan on the budget cuts, but announced early that he was sticking with his party this time. The White House left him alone -- not even a phone call, like the one he got from Reagan last month.

From Wilson's vantage point, the calls from constituents that kept his staff busy this week were genuine and spontaneous. "Reagan just has their hearts," he said. The Forty-Nine Who Voted With the Other Side

Following are the names of the 48 Democrats who voted for, and the one Republican who voted against, the tax-cut plan favored by President Reagan. Two House members did not vote. DEMOCRATS VOTING FOR

Atkinson (Pa.). Barnard (Ga.). Biaggi (N.Y.), Boner (Tenn.), Bouquard (Tenn.), Bowen (Miss.), Brinkley (Ga.), Byron (Md.), Chappell (Fla.), Daniel (Va.), del al Garza (Tex.), Dicks (Wash.), Dyson (Md.). English (Okla.), Evans (Ga.), Fountain (N.C.), Fuqua (Fla.).

Ginn (Ga.), Glickman (Kan.). Gramm (Tex.). R. Hall (Tex.)j, S. Hall (Tex.), Hance (Tex.), Hatcher (Ga.). Hightower (Tex.), Hubbard (Ky.), Huckaby (La.), Hutto (Fla.). Ireland (Fla.), Jones (Tenn.), Leath (Tex.), Levitas (Ga.), Luken (Ohio).

Lundine (N.Y.), McCurdy (Okla.), McDonald (Ga.), Mazzoli (Ky.), Mica (Fla.), Montgomery (Miss.), Mottl (Ohio), Nelson (Fla.), Nichols (Ala.), Roemer (La.), Santini (Nev.), Shelby (Ala.), Stenholm (Tex.), Stump (Ariz.) and Yatron (Pa.). REPUBLICAN AGAINST

Jeffords (Vt.). DEMOCRATS NOT VOTING

Cotter (Conn.) and Minish (N.J).