By the time Vice President Mondale arrived at Jack and Carita Kelleher's farm here today, the shiny black limousine that brought him from Des Moines was caked with mud from the trip over rural roads.

Inside the Kelleher's white frame house, 10 farm couples sat in the living room awaiting him.

"Iowa will be the state the whole world will be watching" next Monday, the vice president said. "Iowa will be the first state where people decide about the future of our country."

Beginning a final three-day campaign swing on behalf of President Carter before next Monday's Iowa precinct caucuses, Mondale preached this message to Iowans throughout the day: Turn out Monday night at your precinct caucus to help your friend Jimmy Carter and show the world you support the president's decision to "stand up to the Russians."

Between now and Friday, Mondale will travel many a muddy country road, voicing that theme through much of western Iowa. It is an area okf the state thought to be among the strongest for Carter in his contest with his Democratic challengers, Sen. Edward M. Kennedy (D-Mass.) and California Gov. Edmund G. (Jerry) Brown Jr.

Carter campaign officials here are hoping for a large turnout at the Monday night caucuses, and part of Mondale's mission this week is to help accomplish that. Three months ago, with Kennedy far ahead in public opinion polls, it was thought that the president's best chance would be a relatively low turnout that would give his long-established Iowa campaign organization the maximum impact.

But now, with the president ahead in public opinion polls thanks largely to the crisis in Iran and Afghanistan, Carter campaign operatives here say that a turnout of 50,000 to 60,000 Democrats, which they predict for Monday night, will be enough to defeat Kennedy, and that a larger turnout will increase the president's margin.

In 1976, 38,500 Iowa Democrats voted in the precinct caucuses, giving Carter his first victory on his way to the White House.

As he toured the state today, Mondale reiterated his defense of the administration's partial grain embargo against the Soviet Union.

In the Kelleher living room, the vice president leaned forward in his chair and with an earnest expression on his face told the farmers, "We decided we had to sting them in a way that was going to get through."

Mondale used the word "sting" in reference to the embargo and several times, and he got no argument over the decision from the farmers that Carter supporter Kelleher inivited to hear him.

The initial shock of the embargo seems to have worn off here, and the impact has been cushioned by gradually stablizing grain prices in the commodity markets. The farmers here spoke less of the embargo than they did of their concern over soil erosion, a message that Mondale promised to carry back to Washington.