Washington (CNN) President Donald Trump is digging in his heels on his demand for a border wall as the shutdown enters its fourth week, telling aides and allies that he believes he is winning the battle for public support.

Over the last 24 hours, Trump has privately touted a Washington Post-ABC News poll indicating that public support for a border wall has increased to 42% from 34% last year, a source familiar with his comments told CNN.

"He's not going to budge even 1 inch," a source familiar with the President's mindset told CNN.

On Capitol Hill, there are currently no meetings scheduled and no new proposals being traded, aides in both parties say.

But a CNN/SSRS survey published Sunday shows a majority of the public blames the President, with 55% saying he is more responsible for the shutdown than are Democrats in Congress, while 32% say the blame rests mostly with the Democrats.

Read More