The court has up to 180 days to decide whether to uphold or reject parliament's impeachment of the country's first female president on charges ranging from bribery to abuse of power.
Park has been suspended from her duties since the impeachment vote on December 9, with the prime minister taking over.
If the judges back impeachment after hearing from both sides, she will be formally ousted and a presidential election held within 60 days. But any split in the Saenuri Party would drastically reduce its chances in such a poll.
"We've reached a conclusion that conservatives' reform through the Saenuri Party is impossible", prominent lawmaker Yoo Seung-Min told journalists.
A split would also complicate any potential presidential run by outgoing UN Secretary General Ban Ki-Moon, who had been widely expected to compete on the Saenuri ticket.
Thirty-five lawmakers have agreed to break away from the party on December 27, the dissident group said, adding they will try to persuade more legislators to join them.
The group crossed party lines to join opposition parties in passing the motion to impeach Park.
Park is accused of colluding with her confidante Choi Soon-Sil to coerce large companies like Samsung into handing over tens of millions of dollars to two dubious foundations which Choi allegedly controlled and plundered.
Park is also accused of ordering aides to leak state documents to Choi, who has no official title or security clearance, and allowing her to meddle in state affairs including the appointment of top officials.
A special prosecutor has been investigating whether Samsung bribed Choi to win state approval for a controversial merger of two of its units last year.
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