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By Yasmeen Abutaleb and Susan Cornwell

WASHINGTON (Reuters) - Ten state governors seeking to avoid millions of dollars in federal healthcare cuts under Republican plans to replace Obamacare pressed their case in a meeting with Vice President Mike Pence on Sunday, according to two people briefed on the talks.

The governors are worried that repealing former President Barack Obama's 2010 healthcare law without a detailed replacement will take coverage away from millions of Americans and land the states with a large financial hit.

Pressure from governors is just one of the challenges facing President Donald Trump's administration as it tries to

scrap Obama's Affordable Care Act, one of the Republican's signature election campaign promises.

During the hour-long meeting, the governors presented Pence and Health and Human Services Secretary Tom Price with a proposal to reform the Medicaid program for the poor, the sources said.

Under Obamacare, more than 30 states - including about a dozen with Republican governors - expanded Medicaid by allowing those who earned incomes up to 138 percent of the federal poverty level to enroll.

The governors' plan would allow those states to maintain the Medicaid expansion and enable other states to also expand, according to a copy of the proposal seen by Reuters. States could choose to expand Medicaid to any income level at or below 138 percent and retain enhanced federal funding for the program.

The proposal would also give states more flexibility in how they manage their Medicaid programs and cap spending for certain populations.

House Republicans have yet to agree on a single detailed policy proposal and many say it will not be in place before 2019.

On Thursday, a draft Obamacare repeal bill by the House Republicans was available for Republican members of the House Energy and Commerce Committee to read in a room on Capitol Hill but was not publicly released. It was not clear whether the governors' demands were addressed in the latest version of the draft bill.

"The President and Vice President have been very clear that governors and states will play a critical role in the repeal and replacement of Obamacare," said Marc Lotter, a Pence spokesman.

Ohio Governor John Kasich also met with Trump on Friday and briefed him on the governors' plan.

In his address to Congress on Tuesday, Trump said that state governors should be given "the resources and flexibility they need with Medicaid to make sure no one is left out."

Wisconsin Governor Scott Walker and House Ways and Means Committee Chairman Kevin Brady met on Thursday with Republican members of the Senate Finance Committee and discussed the Medicaid expansion.

"We're still a long ways off," Walker said. "The same things they (lawmakers) hear from their members are the same things we hear in the states, is how do you balance states that didn't take the expansion and states that did. How do we make sure we find a good way?" he said.

(Reporting By Yasmeen Abutaleb and Susan Cornwell; Additional reporting by David Morgan; Editing by Caroline Humer and Alistair Bell)