Although Clinton, who has polled well in the past with Latino voters, could win the Puerto Rico primary, her hopes of winning the presidential nomination are fading.
The decision on Saturday by the party's rules and by-laws committee to restore only half the voting rights of Michigan and Florida has been a blow to her presidential hopes.
The party had barred delegates from the two states from voting at the party convention in Denver in August - that will decide the presidential nominee - as punishment for moving their primaries forward to January, against Democratic party rules.
Clinton won the primary battles in both states and pushed for both states to have their delegates reinstated.
The party reached a compromise deal in Washington on Saturday, halving the votes of delegates from Michigan and Florida at the August convention.
The committee rejected a Clinton-backed proposal to seat all the Florida delegates at full strength, then backed compromises seating both the Michigan and Florida delegations while cutting their voting power.
The decision divided Democrats, with one woman loudly telling committee members to "shut up", while another shouted "you stole my vote".
Others vowed they would vote for John McCain, the Republican presidential candidate, rather than for Obama in the presidential election.
Harold Ickes, a senior Clinton aide and member of the committee which approved the deal, said her campaign might challenge the ruling.
"There's been a lot of talk about party unity - let's all come together, and put our arms around each other," he said.
In Puerto Rico, the island's central political issue is its relationship with the US.
Both Clinton and Obama support allowing Puerto Ricans to decide for themselves whether they want to try for statehood or keep their current status as part of the US.
Voting results are expected shortly after 3pm local time (1900 GMT).