German Chancellor Angela Merkel has said there are still serious problems with Poland over voting rights before crucial talks on a new EU treaty.
Merkel met Kaczynski in Germany on Saturday
Germany, the current holder of the EU presidency, wants states to agree to a roadmap for a new constitution at next week's summit in Brussels.
Polish President Lech Kaczynski kept up the threat of vetoing any deal that reduces Poland's voting rights.
Czech PM Mirek Topolanek said he backed Poland after a meeting with Mrs Merkel.
Only the Czech Republic supports Poland on the issue.
Speaking in Luxembourg after meeting Prime Minister Jean-Claude Juncker, Mrs Merkel said: "We still have several serious problems to solve before the council."
But Mrs Merkel insisted that the issue had to be solved at the summit, which begins on Thursday.
On Saturday, Mrs Merkel met President Kaczynski in Germany for crucial talks on the simplified treaty.
'Worth dying for'
French and Dutch voters rejected a proposed EU constitution in 2005.
The new, simplified treaty is expected to address demands for institutional change to help the EU to operate more efficiently.
But Mr Kaczynski has threatened to block efforts to draft it at the summit because of the proposed changes to the voting system.
The BBC's Adam Easton in Warsaw says Poland currently has a good deal compared to its size, but under the "double majority" system it stands to be one of the biggest losers.
Mr Kaczynski says he wants European leaders to discuss what he believes is a fairer alternative - calculating voting rights according to the square root of each country's population, rather than simply according to population.
If Poland is not allowed to have its say, it will use its veto, Mr Kaczynski has warned.
"For the time being, we're each sticking to our positions, yet with the conviction that there must be success next Thursday and Friday," Mr Kaczynski said on Sunday.
The president and his twin brother, Prime Minister Jaroslaw Kaczynski, say their plan "is worth dying for".