Leaders of the Senate Banking Committee and two prominent economists warned yesterday that high federal deficits are likely to drive up interest rates and thereby threaten the nation's economic prospects over the next several years.

Banking Committee Chairman Jake Garn (R-Utah), interviewed on "This Week With David Brinkley" (ABC, WJLA), said the current economic recovery is "threatened by higher interest rates and it could be choked off by these large deficits."

Garn was joined by Sen. William Proxmire (D-Wisc.), the committee's ranking minority member. Proxmire said the nation faces "four or five painful and difficult years" and predicted that unemployment would drop perhaps as low as 8 1/2 percent before both the unemployment and inflation rates start to rise because of the size of federal deficits.

Economist Alan Greenspan, appearning on "Meet the Press," (NBC, WRC) called the deficit problem "priority No. 1 on the economic agenda." But he said he did not share Garn's concerns about rising interest rates limiting the recovery in the short run.

Although short-term interest rates are likely to "rise modestly," Greenspan said the current recovery is "so brisk at this stage that its exceedingly unlikely" that a 1 or 2 percent rise in short-term rates would alter the economic picture over the next six months.

But unless federal deficits can be cut, Greenspan said, the nation "will not have the type of very consistent long-term growth" in 1984 and 1985 that could otherwise follow a recovery like the one currently under way.

Greenspan said he did not think Congress would act to cut spending before the 1984 election. "I don't think it will be resolved in the next 18 months," Greenspan said. "But it sure better be after that."

Like Greenspan, economist Henry Kaufman, managing partner at Salomon Brothers, called on the administration and Congress to cut domestic spending. In particular, Kaufman--who also appeared on the Brinkley program--said both the public and private sectors should eliminate the indexation of virtually all payment programs.

On another matter, Greenspan said there was little that could be done at this point to avoid higher telephone rates in light of the break up of American Telephone & Telegraph Co. and the simultaneous deregulation of the telephone industry.

Greenspan, who was chairman of the Council of Economic Advisers during the Ford administration, said it was "probably a mistake" to break up AT&T. The antitrust suit that led to the break up was filed in 1974 during Ford's administration.