Republicans yesterday unveiled the first phase of a television ad campaign that will cost more than $10 million and has look-alikes for Jimmy Carter and House Speaker Thomas P. (Tip) O'Neill Jr. leaving the nation's economic problems to Ronald Reagan in a "last will and testament."

"To Ronald Reagan we leave the recession," an actor portraying a lawyer reads in one ad. "Inflation at 12.4 percent and rising. Gas prices sky high. Government spending money like it was going out of style."

As the O'Neill actor chortles loudly and the Carter actor looks stoically on, the lawyer adds, "To the Republicans in Congress we leave the real problems."

Democrats promptly labeled the 30-second spot, one of two ads Republicans plan to air at a cost of $1.7 million, "a lie" and asked that television stations and networks refuse to broadcast it.

O'Neill objected to the ads "as degrading the office of the presidency." Noting that the Republican campaign is built around the theme "Republicans are beginning to make things better," he added: "My question is better for whom? It's only better for the wealthy."

The two ads released yesterday are the first phase in a three-pronged television offensive that Republicans plan during the congressional elections. They were to begin airing immediately. A second phase of ads, directed at specific problems like unemployment, Social Security and agriculture, is to begin May 26.

In addition, Republicans have set up an elaborate system to market "generic commercials" for about 50 GOP candidates around the country who cannot afford to hire advertising agencies to make their own ads.

The party has budgeted more than $10 million for the television campaign, although Rep. Guy Vander Jagt (R-Mich.), chairman of the House Republican campaign committee, said, "We will spend whatever is necessary to get our message to the American people."

Democrats, without the same resources to finance their own ads, have long feared the impact on next fall's congressional races of a "negative" ad campaign. A similar campaign, featuring the same actor portraying O'Neill running out of gas, attracted widespread attention in 1980.

Rep. Tony Coelho (D-Calif.), chairman of the House Democratic campaign committee, sent a telegram to television networks and local stations urging them not to air the ads.

"To claim, as the Republicans' ad does, that Ronald Reagan was left a recession is a lie," he said. "That statement is false, misleading and factually inaccurate. The truth is that the unfair economic policies of the Reagan administration brought about the recession--the worst since the Great Depresssion."

Vander Jagt said GOP survey data show that two of every three Americans "identify the recession as Jimmy Carter's, not Ronald Reagan's," but he added that by the same ratio they believe inflation is running at a higher rate than a year ago, although it has come down.

A second commercial shown at a news conference pictures two couples embarking on a vacation in a dust-covered camper that they haven't been able to use for two years because of high prices. "President Reagan and Republicans in Congress created programs that brought inflation down--from more than 12 percent to less than 4," a voice says in the ad.

Vander Jagt said the ads will be aired on local stations and on two of the three major networks. He said CBS had refused to air them. Spokesmen for ABC and NBC said no decision had been made on whether to accept them.