When Bartiromo asked if the Republican Party really wants the president to succeed, Trump responded, "I think that a vast majority of Republicans are on board with the president's agenda".
Nearly 6 in 10 people think the Republicans should work with Democrats to improve the health law.
The president has been smarting from the Senate's failure to pass an overhaul of the Affordable Care Act, a long-standing priority for the GOP and a marquee campaign promise from Trump past year.
Most (60%) of the public say that President Trump and Republicans in Congress control the government and are responsible for any problems with the ACA going forward, twice the share (28%) who say President Obama and Democrats in Congress are responsible for such problems.
On Thursday, Trump's main mainstream media ally Fox News joined the president in lashing out at McConnell and congressional Republicans.
While some have speculated that picking a fight with McConnell is risky, particularly because McConnell controls the Senate's agenda, Paul said he didn't think the public feud would deteriorate their relationship or the relationship Trump has with Congress. The failure has led to huge infighting within the GOP: Trump wants another vote, Senate Majority Leader Mitch McConnell wants to move on, and Speaker Paul Ryan is eager to work on tax cuts for the rich.
On three separate attempts in late July, McConnell fell short of the 50 GOP votes he needed to pass legislation scrapping Obama's law.
"I talk to the president a lot", he said.
Only 17 percent of the public and 40 percent of Republicans think the Trump administration should take steps to make the health law fail, the survey said. For a White House that often seems more concerned with cementing support from Trump's loyalists than embracing the political center, that might help explain the president's persistence on the issue. Analysts say that would roil insurance markets because fewer healthy people would buy policies, leaving them with greater proportions of expensive, seriously ill customers.
The companies use the money to trim out-of-pocket costs for deductibles and copayments for around 7 million low- and middle-income people.
A KFF poll released Friday finds that 52 percent of Americans now have a favorable view of the 2010 healthcare law, a 2-point increase from the same poll last month.
Designed and analyzed by public opinion researchers at the Kaiser Family Foundation, the poll was conducted from August 1 - 6 among a nationally representative random digit dial telephone sample of 1,211 adults.