Several Republican senators have indicated that they would be willing to support a health care bill that funds Planned Parenthood or some abortion services, Fox News has learned.

The GOP is worried that any bill to repeal and replace ObamaCare would have to be carefully structured to hold the support of moderate and conservative Republicans. However, the apparent concession by conservatives might give leadership more room to maneuver.

The pressure is on Senate Republicans to try to move a bill to repeal and replace ObamaCare before the Fourth of July recess. The House of Representatives passed its own bill, the American Health Care Act, last month.

Fox News has also learned that Senate GOP leaders have been sending policy proposals to the Congressional Budget Office for evaluation and scoring. However, a full bill was not expected to be presented at the weekly Republican luncheon Tuesday.

Senate Republicans are winnowing down policy options in an effort to get the necessary 51 votes to pass any health care legislation. Some believe any bill will only get 50 votes, necessitating a tie-breaking intervention by Vice President Mike Pence.

Meanwhile, the government said Monday that about 16 percent of consumers who signed up for coverage this year through Healthcare.gov and its state counterparts had canceled their plans by early spring.

Figures released from the Health and Human Services department show that 10.3 million people were signed up and paying their premiums as of March 15. That's 1.9 million fewer than the 12.2 million who initially signed up during open enrollment season, which ended Jan. 31.

In the first part of last year, the dropout rate was similar, about 13 percent. It increased as the year went on. Monthly enrollment averaged about 10 million people in 2016.

Some of the main reasons for dropping out include finding job-based insurance, problems paying premiums, and becoming eligible for Medicare.

A new analysis from HHS also found higher dropout rates in areas where insurers have left the program. About one-third of U.S. counties only had one participating insurer this year, and next year there may be areas with no available carrier.

The Trump administration said the numbers are a sign of continuing problems with Obamacare, such as sharp premium increases and the departure of some major insurers that suffered financial losses. Democrats have accused Trump of trying to "sabotage" Obama's signature domestic achievement

Fox News' Chad Pergram and Mike Emanuel contributed to this report. The Associated Press also contributed to this report.