WASHINGTON - President Donald Trump pressed Republican lawmakers on Tuesday to support a new attempt to overhaul the US healthcare system, but struggled to attract party moderates who feared a backlash from voters who could lose insurance benefits.Most Republicans in the conservative House Freedom Caucus faction have gotten on board with the new bill, which Democrats are vowing to oppose. A lobbying battle to influence Republican moderates was under way involving both conservative and liberal political groups."It's close. We're getting there," said Representative Tom MacArthur of New Jersey, a moderate Republican who brokered the deal with hardline conservatives that revived the healthcare legislation.The stakes are high for Trump, who vowed during his 2016 campaign to repeal and replace the Affordable Care Act, commonly known as Obamacare. Over the past several weeks, he has repeatedly set deadlines for the House of Representatives to pass a healthcare bill. So far, the Republican-led House has fallen short of securing the necessary votes.Representative Mark Meadows of North Carolina, who heads the House Freedom Caucus that helped block passage of the first healthcare bill, said Republicans were still "a handful of votes away."The current bill would allow states to opt out of Obamacare provisions that force insurers to charge sick and healthy people the same rates. That is seen as a concession to the Freedom Caucus, which has endorsed the new measure.