Separatists won a majority of seats in the 135-seat Catalan parliament for the first time in a September election in the wealthy northeastern region of Spain which is home to 7.5 million people.
Mas's "Together for Yes" secessionist alliance, which won 62 seats, needs the backing of the smaller CUP grouping to remain at the helm in Catalonia.
But the CUP, which opposes Nato and EU membership, has refused to back Mas to date because of his austerity policies of recent years and his party's links to corruption scandals.
With a January 9th deadline looming for Catalonia to elect a leader and form a new government, CUP members held a vote to decide a final position, which resulted in an extraordinary impasse.
Half of the CUP grassroots members at the assembly - 1,515 - voted in favour of allowing Mas, a conservative, to head the next government, while another 1,515 voted against.
Now it is up to the party's leadership to make a final decision at a meeting on January 2nd.
In order to be re-elected head of the regional government in a vote in parliament, Mas would need just two more CUP lawmakers to back him.
If the Catalan parliament does not elect a leader and form a new government by January 9th, it must call fresh elections. They would be the fourth in the region since 2010.
"The numbers are diabolical but beyond that we are faced with a political challenge, a challenge to debate and find solutions," said CUP parliamentary leader Antonio Banos.
To coax the CUP into backing Mas, "Together for Yes" on Tuesday promised a series of social reforms such as extra financing for homeowners facing eviction and school meals for poor children.
While separatists have not agreed on the formation of a new government, last month they approved a resolution that calls for the creation of an independent Catalan republic within 18 months, laying down a major challenge to the central government in Madrid.
The divisions among Catalonia's secessionist camp appear to have benefited new anti-austerity party Podemos, which came first in the region in Spain's general election on December 20th.
Podemos wants Catalonia to remain a part of Spain but is in favour of allowing an independence referendum in the region like the ones held in Scotland in 2014, and in Quebec in 1980 and 1995, which both resulted in votes for the "No" camp.
All other national parties refuse to allow a referendum, judging it against the constitution.
Polls show that most Catalans support a referendum on independence, but are divided over breaking from Spain.