Theresa May is on track to win 304 seats, 22 seats short of a 326-seat majority, according to a daily projection by YouGov.
The Conservatives had 330 seats when the snap election was called in April.
On Monday, YouGov said its model suggested the Tories were on course to win 305 seats.
Labour is likely to win 266 seats, YouGov's model showed, down from 268 on Monday.
But another model, produced by Lord Ashcroft Polls, last week predicted the Conservatives were on course for a majority.
A new Survation opinion poll suggests the election race is neck and neck, with the Conservative lead over labour being slashed to a single point.
The poll for Good Morning Britain (GMB) put the Tories on 41.5 per cent with Labour on 40.4 per cent.
If such a result were replicated on Thursday it would put the Conservatives' majority in Parliament in jeopardy.
But opinion polls by other leading polling firms have given wider leads for the Conservatives in recent days, ranging as high as 11 and 12 points.
Three weeks ago, a series of surveys showed Ms May was on course for a landslide parliamentary majority which she called to secure a strong mandate for Brexit talks.
But her campaign began to struggle after she proposed a plan to make elderly people pay for more of their social care, a so-called "dementia tax," even though she moved quickly to say there would be a limit on the amount of costs that people would face.
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