"D-Day is Tuesday," he told Face The Nation host Bob Schieffer. "Whoever has the most delegates after Tuesday should be the nominee."
Richardson deferred from announcing a personal endorsement of either Hillary Clinton or Barack Obama ("I'm legitimately torn," between the two, he said), but suggested that the leader after this week's primaries will have the presumptive title.
He also called for a positive Democratic race rather than one marred by negative ads or name-calling. "We have to have a positive campaign after Tuesday," Richardson said.
"I think we've got to be ready for a very strong John McCain. Republicans are united right now. They don't have a divisive primary. It looks like the tone of our campaign is heading much too negative. And I want to see us after Tuesday basically come together and see where we are and move on to the general election.
"This campaign is getting much too negative. The American people want us to be positive. They want us to talk about issues. And I'm just worried that the tone of this campaign has gotten excessively negative. And it may hurt us in November."
Also appearing on the program, Sen. Christopher Dodd, D-Conn., advised the candidates against bickering.
"It doesn't serve our interests here to be demeaning the other candidate, in my view," he told Schieffer. "And I'm worried about these ads in a sense creating that kind of an environment."
However, Sen. Evan Bayh, D-Ind., who supports Clinton, did not think her campaign's controversial television ad (in which voters are asked to consider who would best handle being alerted to a world crisis at 3 a.m.) is negative.
"It's not a question of if we're going to be attacked again by al Qaeda; it's a question of when," he said.
"It is a dangerous world. And we need to have a debate about who is best prepared, for this important moment, to be commander in chief."
Read the full "Face the Nation" transcript here.