President Richard Nixon and Secretary of State Henry Kissinger discussed bombing the dike network in a 1972 conversation on Operation Linebacker II, later published by Daniel Ellsberg:

Nixon: We've got to quit thinking in terms of a three-day strike [in the Hanoi-Haiphong area]. We've got to be thinking in terms of an all-out bombing attack - which will continue until they - Now by all-out bombing attack, I am thinking about things that go far beyond. I'm thinking of the dikes, I'm thinking of the railroad, I'm thinking, of course, the docks.

Kissinger: I agree with you.

President Nixon: We've got to use massive force.

Two hours later at noon, H. R. Haldeman and Ron Ziegler joined Kissinger and Nixon:

President: How many did we kill in Laos?

Ziegler: Maybe ten thousand - fifteen?

Kissinger: In the Laotian thing, we killed about ten, fifteen.

President: See, the attack in the North that we have in mind, power plants, whatever's left - POL [petroleum], the docks. And, I still think we ought to take the dikes out now. Will that drown people?

Kissinger: About two hundred thousand people.

President: No, no, no, I'd rather use the nuclear bomb. Have you got that, Henry?

Kissinger: That, I think, would just be too much.

President: The nuclear bomb, does that bother you?...I just want you to think big, Henry, for Christsakes.

It was certainly discussed, informally, and studied by the JASON group, who concluded that tactical nuclear weapons would not materially aid the US case in Vietnam, and would actually be endangering to US strategy.

You can read about the JASON study here. Basically they argued that they would be ineffective at stopping the North Vietnamese even if they were unilateral. If the Soviets or Chinese took it as an opportunity to equip the Vietnamese with their own tactical weapons, then it would be absolutely disastrous for the US, who was far more reliant on fixed fortifications and bases than the Vietnamese.

In 1967 the physicist Freeman Dyson, a member of the JASON scientific advisory group to the military, heard at a cocktail party General Maxwell Taylor, LBJ's closest military advisor, shooting his mouth off about the desirability of using nuclear weapons in South Vietnam.

Shocked, Dyson and three other JASON members led by Robert Gomer wrote a report that, while couched in dispassionate military analysis, aimed "to show that using nuclear weapons would be immoral folly, and would set an awful precedent." Several of the authors later admitted they never would have written the report if it had been possible that it could have concluded favorably.

They argued that there were very few good enemy targets for tactical nuclear weapons, while Russia and China might retaliate directly or through Vietnamese proxies with vastly more effective nuclear strikes of their own against concentrated, high-value US bases in Vietnam. In the worst case, U.S. fighting capacity in Vietnam might in a matter of hours be "essentially annihilated" and the majority of U.S. service members in that country killed. There were also proliferation and political concerns.

Dyson and colleagues never found out who read their report or how seriously it was taken. In 2002 an organization called the Nautilus Institute obtained a lightly redacted version of the report under FOIA and put it on the Internet along with a quite nice website.

Yes, it was certainly discussed, as others have said, and the closest time that U.S forces came to the deployment of tactical nuclear weaponry was during the siege of Khe Sanh.

Khe Sanh was a Marine Airbase which housed III Marine Amphib. Force, Army 1st Cav. and USAF elements. Shortly before the Tet Offensive the base came under a massive assault by two to three NVA divisions.

The base was under siege for something like five months and it was hammered with NVA artillery, mortars and rockets. During the siege, Westmoreland-the U.S strategic commander was prepared to deploy nuclear or chemical weapons to avoid the base falling. a plan was put to Pacific Command for the deployment of low-yield nuclear weaponry which was ultimately denied.

Rather, the base held and the forces holding it were reached by a ground reinforcement column and the NVA forces backed off. Ironically, the base was dismantled shortly after the successful defense.

It was actually decided that the deployment of nuclear weaponry would be ineffective as the terrain greatly hampers the destructive capabilities and after-effects of the detonation.

Follow up question: were small yield tactical nuclear weapons deployed and used in the Vietnam War?

There was a discussion about using an atomic bomb during Operation Vulture. 1954, French - Indochina War.

One version of the plan envisioned sending 60 B-29s from US bases in the region, supported by as many as 150 fighters launched from US Seventh Fleet carriers, to bomb Giap’s positions. The plan included an option to use up to three atomic weapons on the Viet Minh positions. Radford, the top American military officer, gave this nuclear option his backing. US B-29s, B-36s, and B-47s could have executed a nuclear strike, as could carrier aircraft from the Seventh Fleet.[1] U.S. carriers sailed to the Tonkin gulf, and reconnaissance flights over Dien Bien Phu were conducted during the negotiations. According to Richard Nixon the plan involved the Joint Chiefs of Staff drawing up plans to use 3 small tactical nuclear weapons in support of the French.[2]

I'm on mobile so I cannot directly link to this video at the appropriate time. Go to 4:00 in this video to hear French Foreign Minister Georges Bidault discussing a conversation with US Secretary of State John Foster Dulles (1954) about the use of Atomic Bombs. Hearts and Minds - 1974