Trump said Sunday on his Twitter account, just days after the House narrowly voted to repeal the seven-year-old health law popularly known as Obamacare.
Gillibrand and Schumer's remarks came hours after Trump urged Senate Republicans to support the House plan in a Sunday morning Twitter post.
"Speaker Ryan today said that he hoped that the Senate would improve the House bill", Collins said.
The health secretary said Republicans believe insurance under their plan "is going to be more affordable".
Sen. Kirsten Gillibrand called on Senate Republicans to reject the U.S. House plan to repeal and replace the Affordable Care Act, calling the measure a "cruel and risky bill", that would leave millions of Americans "stranded without the health care they need".
"Republican Senators will not let the American people down!"
"That is an important issue to me because I don't think that low-income women should be denied their choice of health care providers, for family planning, cancer screenings, for well women care (but) it's not the only issue in this huge bill", she said. Although the current bill was approved before the nonpartisan Congressional Budget Office could review the measure, Gillibrand cited a study the office issued in March that indicated 24 million Americans would lose their health coverage over the next decade under an earlier version of the bill that was never voted on.
A political nonprofit aligned with House Speaker Paul Ryan is offering air cover to Republicans who backed the House effort to repeal and replace Obamacare, launching a new national ad buy that begins on Monday.
"We're going to draft our bill, and I'm convinced we will take the time to do it right", she said. Some senators have already made clear that they intend to make major changes to the bill, which passed Thursday. It would dilute consumer-friendly insurance coverage requirements, like prohibiting higher premiums for customers with pre-existing medical conditions and watering down the subsidies that help consumers afford health insurance. Trump tweeted. "ObamaCare premiums and deductibles are way up - it was a lie and it is dead!"
The bill would lead to major cuts to the Medicaid program, which funds care for the poor and disabled.
"But most importantly, it's us trying to fix a real problem that real people are experiencing in this country".
Conservative Rep. Raul Labrador, R-Idaho, drew boos Friday at a public meeting for his response to a constituent who said the House bill tells people on Medicaid to "accept dying". "The Senate will complete the job".
Collins and Ryan appeared on ABC's "This Week" and Priebus was on "Fox News Sunday".