President Carter's proposal to allow voting registration on the day of election faces significant changes in the House, Supporters of the measure indicated yesterday.

Rep. Frank Thompson Jr. (D-N.J.) said he expects the legislation will be amended next week to allow states to adopt same-day registration on a voluntary basis in 1978, making it mandatory in 1980.

Vice President Mondale, handling the measure for the administration called such a two-year delay "a very live option."

"Theres' a distinct possibility that accepting an amendment of this sort is the only wall to forestall delaying the whole thing until 1980," said Thompson, chairman of the House Administration committee.

The committee yesterday wound up five days of hearings at which witnesses warned of possible vote fraud, administrative foul-ups and long lines in the polling places that could discourage voters.

Thompson said he believes the dangers of fraud are highly exaggerated. But he shares the concerns of local election officials who want "start up money" to hire extra precinct judges and deputies.

Amendments to provide these funds, running into millions of dollars, will be offered next week when the committee meets to mark up the bill. There also are likely to be amendments to require a uniform system of voter identification at the polls and to limit the number of people that an already-registered voter can vouch for as residing in the precinct.

Mondale told reporters the administration would accept such changes. But he rejected arguments that the plan would be wide open to fraud. "There is utterly no evidence there has been fraud" in the four states already using election day registration, he said, adding that the bill contains stiff penalties to deter he organization of mass illegal registration.

Thompson has promised "a very tight bill" that will allay the fears of those who fear fraud and administrative abuses. But even with amendments, the New Jersey Democrat said, same-day registration faces a close test in the House.

By accepting a number of amendments offered by the Republican elections specialist, Rep. William Frenzel of Minnesota, the Democrats hope to gain enough GOP votes to offset the certain loss of some Southern Democrats. Many Southern states have restrictive registration procedures and relatively low vote turnout. Some students of voting patterns believe that it is these states that could have the greatest increase in turnout if election-day registration is allowed.

Republicans seem to be of two minds about the measure. House Minority Leader John J. Rhodes of Arizona announced his support for the plan when it was unveiled by President Carter, but this position has proved highly unpopular with Rhodes' GOP colleagues.

Many Republicans in the House want to oppose the measure outright believing that its enactment poses a serious threat to the GOP. Other members, following the lead of Rhodes and Frenzel, say that passage is inevitable and are trying to do their best to improve the legislation by tightening fraud detection procedures.

Thompson also is on the spot politically. He lost his first major bill in 23 years when the House rejected the common site picketing bill after it had sailed through his committee.

"Toppie is determined that he's not going to lose another one," said a source close to the committee. "He won't take the bill up on the floor until it's in shape and he's sure he has the votes."

Any delays could imperil the outcome of the legislation, which faces an even stiffer test in the Senate, where a committee begins hearings next week. The administration is known to fear a possible filibuster by Sen. James B. Allen (D-Ala.) when the legislation reaches the floor.

Critics of the proposal, which Carter calls "universal registration," held the upper hand this week in testimony before the House Administration Committee.

The most negative response came from officials of Project Leap (Legal Elections in All Precincts), an antivote-fraud organization widely credited with reducing vote fraud in Chicago through the recruiting and traning of honest elections judges.

Sheldon Gardner, a former prosecutor with the Cook County state attorney's office, said that the gains made in Chicago during the last five years would be wiped out by on-site registration.

A number of local elections officials said that the bill would impose heavy burden without providing the money to pay for the added responsibility.