Mondale, Reagan: a tale of 2 coattails.

The campaign of first-term Democratic Rep. Thomas R. Carper of Delaware has been urging vice-presidential nominee Geraldine A. Ferraro to visit. She has ''dynamic zip,'' according to a member of the Carper camp, and she might help fend off a challenge by Republican Elise du Pont, wife of Delaware Gov. Pierre S. du Pont IV.

But members of the Carper campaign are not holding their breath for a visit from the Democratic presidential nominee.

In a lopsided political year in which challenger Mondale still lags far behind, many Democratic candidates are trying to keep a safe distance from their presidential ticket, while Republicans are clinging close to Reagan and beginning to talk gleefully about a GOP sweep down the ballot next November.

Walter F. Mondale ''is not personally very popular'' in Delaware, said Representative Carper's press aide recently. ''I don't think it would necessarily hurt us. I think there is a question as to whether it would help us.''

Earlier this month when former Vice-President Mondale visited Oregon, another embattled Democrat, Rep. Les AuCoin, stood at the nominee's side despite the fact that his mostly prosperous district favors President Reagan.

''Politically, it wasn't the safest thing to do,'' Representative AuCoin, an early Mondale supporter, said later of the joint appearance. ''There are times you have to stick your neck out.''

On Capitol Hill, Rep. Bill Alexander (D) of Arkansas, who chairs the Mondale effort in his state, sported a ''Mondale'' button and joked that it ''separates the men from the boys.''

Mondale acknowledged the concern of his party's lawmakers during a speech to House Democrats just before the campaign officially began. As recalled by Rep. Tony Coelho (D) of California, the former vice-president said that when he visits congressional districts, ''I can always tell if I'm not doing well'' because the Democratic lawmakers have ''conflicts'' preventing them from joining him. Lately, some Democrats have been pleading ''conflict,'' although their campaign staffs also blame the Mondale operation for giving late notice.

When Mondale when to Ashville, N.C., last month, Democratic Gov. James B. Hunt Jr., who is running against Republican Sen. Jesse Helms, was on vacation. On a Mondale visit to Arkansas, he met only briefly with incumbent Democratic Sen. David Pryor, who had to rush away to other commitments.

''You don't want your campaign to get wrapped up in the presidential race,'' says an aide to Rep. James R. Jones (D) of Oklahoma, the House Budget Committee chairman whose conservative district is overwhelmingly pro-Reagan.

Meanwhile, many Republican candidates are reaching out for possible Reagan coattails.

When President Reagan unleashes an attack on the Democratic House, for the failure to pass a balanced budget amendment or anti-crime bills, the GOP congressional campaign committee takes down his words. Within hours the message goes out on the Republican computer service to their candidates for use in their campaigns.

Steve Lotterer, a spokesman for the National Republican Congressional Campaign Committee, pointed to a recent poll showing that 49.5 percent of voters , up from 44 percent in July, now say they plan to vote Republican in congressional races.

But for all the signs, the big victory for the Republicans is still only speculation. The so-called ''generic'' voter poll is not seen as a very accurate predicter. And many observers of congressional elections are still foreseeing only slight changes in the House, which now has a nearly 100-seat margin for the Democrats, and little change in the Senate, where the GOP has a 55 to 45 majority.

''We have no demonstratively perfect evidence'' that a popular president will win elections for other candidates on the ballot, says Norman J. Ornstein, a congressional expert at the American Enterprise Institute, a Washington think tank.

In 1980, President Reagan won handily, and the Republicans also gained 33 seats in the House while taking over the majority in the Senate. But in many districts the Republican challengers outpolled candidate Reagan in 1980, leaving the question of whether there were coattails.

''Most of the people who won in 1980 were people who had good campaigns of their own,'' says Bernadette Budde, political director of the Business-Industry Political Action Committee and a close observer of congressional elections since 1972.

Although she sees some Republican challengers gaining strength, Ms. Budde is cautious in predicting big shifts, partly because there are only 27 open seats at stake in the House this year and partly because there are more ''healthy incumbents.''

Moreover, while the Republican Party is touching on the theme that President Reagan will need Republicans on Capitol Hill, Ms. Budde says that just may not be enough.

''If Ronald Reagan would make 30 stops in 30 congressional districts and do parades, walking arm in arm with candidates, then I think it would make a big difference in some of these districts,'' she says. But without it, ''I don't know.''