CARTER LOST ILLINOIS in 1976, and this year is struggling to avoid damage in the bitter Democratic civil war between his backer, state Sen. Richard M. Daley, running for state's attorney in Cook County, and Chicago Mayor Jane Byrne. As if that were not enough, he is facing two native Illinoisans in Reagan and Anderson. Despite all that, he seems to be gaining, to the point where some recent polls show him narrowly in front. A recent poll showed Anderson third in his own congressional district, with only 22 percent. Nonetheless, he is hurting Reagan in the high-income GOP "collar counties" around Chicago, where Reagan needs big majorities. However, Reagan is running better that Ford did in the southern half of Illinois. GOP tradition and organization-finance advantages could still pull him through.

Secretary of State Alan J. Dixon (D), the party's best vote-getter in recent years, is running about 10 points ahead of Lt. Gov. David C. O'Neal (R) in a lackluster race to succeed retiring Sen. Adlai E. Stevenson III (D).

No overall change is expected in the House delegation, but there will be some new faces. State Sen. Harold Washington (D) defeated Rep. Bennett M. Stewart (D) in a primary, and publisher Gus Savage (D) will succeed retiring Rep. Morgan F. Murphy (D) in two South Side Chicago districts. State Sen. Lynn M. Martin (R) is favored over County Treasurer Douglas R. Aurand (D) in Anderson's old Rockford seat. INDIANA (13)

TOP-OF-THE-TICKET GOP strength threatens two longtime Democratic members of Congress, Sen. Birch Bayh (D) and House Majority Whip John Brademas (D). Reagan is favored over Carter by landslide proportions and Lt. Gov. Robert D. Orr (R) is almost as strong a bet against industrialist John A. Hillenbrand Ii (D) to succeed the enormously popular retiring governor, Otis R. (Doc) Bowen (R). Hillenbrand beat a labor-backed candidate in the primary and has not healed the intraparty wounds.

Bayh, a third-termer with strong labor support, is being pressed hard by Rep. Dan Quayle (R), a well financed young conservative with ties to the Pulliam publishing family and Bowen's personal endorsement. Bayh is also the target of anti-abortion and other conservative movements, but he is a dogged, skillful campaigner. The latest GOP poll gives him a 4-point lead and no one thinks he will be easy to dislodge.

After 11 terms in the House and several close races, John Brademas may have found in 1980 a combination even he cannot cope with: tough economic times in South Bend, a powerful GOP tide in the state and an opponent, 27-year-old businessman John P. Hiler, who is challenging him on the issues. Brademas is counterattacking strongly, with plenty of funds, but it's a cliffhanger.

Other incumbents with potentially serious challenges if the GOP flood waters rise are Reps. Floyd Fithian (D), David W. Evans (D) and Andy Jacobs (D). Quayle's former aide, Daniel R. Coats (R), is expected to take over his boss's House seat. IOWA (8)

IOWA HAS A HABIT of helping Carter in the winter caucuses but not the November election -- and so it seems this year. It launched him in 1976 and gave him a vital victory over Kennedy this year. But the grain embargo that was initially accepted has become so unpopular that even rising farm prices cannot cure the problem. Carter may have cut Reagan's 17-point lead in an August Des Moines Register Iowa poll in half, but he is unlikely to come much closer.

Sen. John C. Culver (D), seeking a second term against Rep. Charles E. Grassley (R), has come back from a 17-point summer deficit to dead-even in the polls. In 1978, another conservative, Roger Jepsen, backed by anti-abortion groups, defeated Culver's fellow liberal senator, Dick Clark, but Democrats think a higher presidential-year turnout and Culver's own tough debating and campaigning may withstand the challenge from Grassley and his grassroots organization.

The House picture is mixed, with the betting there will be no change. Veteran Neal Smith (D) has a stronger-than-usual challenge, and Berkley Bedell's (D) bid for a fourth term is shadowed by a continuing government investigation into possible customs violations by his fishing tackle business. Grassley's House seat has been Republican since 1934, but Lynn Cutler (D), a county commissioner and close Carter ally, is giving her opponent, former State Rep. Cooper Evans (R), a real battle. KANSAS (7)

REAGAN DIDN'T NEED the embargo issue to carry Republican Kansas, but he has it to help build his margin. Sen. Bob Dole (R), seeking a third term, is equally far ahead of former State Sen. John Simpson (D), who switched parties to make this race and is having to finance it with $100,000 of his own money.

Two House members face serious challenges. Veteran Larry Winn Jr. (R) has a strong opponent in Dan Watkins (D), the former executive director of the state Democratic party, but the district is Republican territory. Freshman Jim Jeffries (R), who has received adverse publicity as a "New Right" eccentric, is opposed by Sam Keys (D), a college professor and former husband of Martha Keys (D), the incumbent Jeffries defeated in 1978. In another district, Pat Roberts (R), an aide to retiring Rep. Keith G. Sebelius (R), is expected to succeed him. MICHIGAN (21)

TARGETED BY THE CARTER forces as one of the few 1976 Ford states he might switch in 1980, it is currently a shade better than even money to remain in the GOP column. Republican polls show Reagan's lead has expanded slightly to 6 points as Republican ticket-splitters have left Anderson, but Democrats insist that Carter has a 50-50 chance to pull it out if Anderson's decline continues. Auto industry unemployment is the worst Carter liability here, but he has strong black support in Detroit and both Bush and Gov. William G. Miliken (R) are still having to work hard to lure GOP moderates to Reagan.

There are a number of close House races. The most threatened incumbents are freshman Democrats Howard Wolpe and Don Albosta, both in Republican territory, and Harold S. Sawyer (R), facing a rematch with Grand Rapids lawyer Dale R. Sprik (D), who lost by only 1,172 votes last time.

Retired Judge George W. Crockett Jr. (D) will take the Detroit seat formerly held by convicted ex-Rep. Charles C. Diggs Jr. (D). The Democrats are likely to retain the seat of retiring Rep. Lucien N. Nedzi, but State Rep. Dennis M. Hertel (D) faces a battle from television talk show host Vic Caputo (R). MINNESOTA (10)

THE "CARTER DIFFERENCE" in Minnesota is Fritz Mondale, who has campaigned in his home state eight times. The early September Minneapolis Tribune poll had it close -- Carter, 34; Reagan, 31; Anderson, 19 -- but local observers think the margin has widened considerably since then.

There is no Senate race, but each party has a shaky House seat. Republicans are very confident that Vin Weber (R), a newspaper publisher and campaign manager with backing from the strong anti-abortion force, can defeat Archie Baumann (D), the aide to the retiring Rep. Richard Nolan (D). But Democrats see a chance former state Rep. Gene Wenstrom (D) can win his rematch with Rep. Arlan Strangeland (R), a narrow victor in 1978. MISSOURI (12)

CARTER HAS BEEN gaining through September and is virtually at the point of overhauling Reagan in a state he won last time. Democratic candidates have been keeping their distance from Carter, while Republicans were aligning themselves closely with Reagan. But there is a Democratic tradition in the state, which could help keep it in Carter's column. For now, a tossup.

The governor's race is a rematch of the very close 1976 contest between Gov. Joseph P. Teasdale (D) and ex-Gov. Christopher S. (Kit) Bond (R), neither a popular figure in his own party.

Sen. Thomas F. Eagleston (D) rates as a solid favorite for a third term over St. Louis County Executive Gene McNary (R), a credible candidate suffering from lack of statewide identity.

Republicans are looking for House gains. One could come in the seat of retiring Rep. Richard H. Ichord (D), where State Rep. Wendell Bailey (R) is rated even or a bit ahead of State Rep. Steve Gardner (D). The other seriously challenged Democrats are Reps. Harold L. Volkmer and Bill D. Burlison. NEBRASKA (5)

REAGAN IS a sure winner and Republicans are very optimistic that businessman Hal Daub (D) will defeat County Commissioner Richard J. Cavanaugh (D), giving the GOP a sweep of the House delegation. NORTH DAKOTA (3)

OF THE FOUR TOP RACES, Republicans are cinches in two and Democrats narrowly favored in a pair. Reagan is miles ahead. The Minot Daily News September poll showed Reagan 48, Carter 24, Anderson 13.

In the contest to succeed retiring Sen. Milton Young (R), Rep. Mark Andrews (R) led Kent Johanneson (D), a wealthy oil broker and developer, 69 to 25. The campaign has been nasty, but Andrews' lead is solid.

Gov. Arthur A. Link (D) was narrowly ahead of Attorney General Allen I. Olson (R) in his bid for a third term, and Tax Commissioner Byron L. Dorgan (D) had a similarly small margin over state Sen. James Smykowski (R) in a liberal-conservative fight for Andrews' old House seat. Dorgan is better known, and Democrats count this as a likely pickup. OHIO (25)

CARTER WON OHIO by only 11,116 votes last time, and so far he has been unable to dislodge Reagan from the favorite's role in what could be a fateful switch. A recent private poll showed at Reagan 41, Carter 33, Anderson 12. sAnderson is part of Carter's problem, but so is unemployment in the auto and steel industries and a drastic weakening of his support in southern and southeastern Ohio, where his Dixie origins gave him more support in 1976 than Democrats usually find.

Sen. John Glenn (D), a Carter booster, is breezing to a second term over state Rep. James E. Betts (R). Democrats hope State Sen. Harry Meshel (D) can defeat freshman Rep. Lyle Williams (R) in traditionally Democratic Youngstown, but must worry about Reps. Thomas A. Luken, Thomas L. Ashley and the open seat vacated by retirinig Charles A. Vanik (D), where state Rep. Dennis Eckhart (D) faces ex-probate judge Joseph J. Nahra. SOUTH DAKOTA (4)

ASTONISHINGLY, CARTER CAME within 4,437 votes of carrying South Dakota in 1976, but that was before the Russian grain embargo, and this year the farmers are voting for Reagan, who should win easily.

Sen. George S. McGovern (D) in his bid for a fourth term, is still in the latest polls and may well rank as the most endangered Democratc incumbent. tMcGovern has attacked Abdnor's support from right-wing groups and his refusal to debate, and apparently will outspend Abdnor, $2 million to $1 million. But the former presidential nominee remains the underdog.

Clint Roberts (R), a former state agriculture secretary, is expected to retain the Abdnor House seat for the GOP. WISCONSIN (11)

CARTER CARRIED Wisconsin by 35,000 votes last time, but with Anderson's poll strength over 20 pecent until recently, Carter has been struggling uphill to catch Reagan. Ex-Wisconsin Gov. Patrick J. Lucey, Anderson's running-mate, may have no edge on popularity in Wisconsin over Vice President Mondale, but this is clearly a state where Anderson could cost Carter vital electoral votes.

The Senate is close -- at least at the moment. Ex-Rep. Robert W. Kasten Jr. (R), who lost in the GOP primary for governor two years ago, came out of the Sept. 9 primary with enough momentum that his own poll showed him leading three-term Sen. Gaylord Nelson (D), 46-44. Nelson is a popular figure and a notoriously slow-starting campaigner, and no one is counting him out yet.

The stiffest House challenges are being thrown at veteran liberal Democrats Robert W. Kastenmeier and Les Aspin, but their challengers, Jim Wright and Kathryn H. Canary, are not established figures in their districts. Freshman Thomas E. Petri (R), victor by 1,200 votes in a 1979 special election, is expected to have an easier time in his rematch with State Sen. Gary R. Goyke (D).