"Here we are, you know, after all this work went on," Hogan told ABC News Chief White House Correspondent Jonathan Karl on "This Week" Sunday. "Both parties were so far apart in the House and the Senate. The problem solvers caucus, some -- some really bipartisan folks on both sides of the aisle brought everybody to the table. They reached an agreement."
"Secretary (Steven) Mnuchin worked together with them and made commitments on behalf of the administration, and then -- not eight months before or even eight days before but after it was passed -- then the president raises these objections? Millions of people are going to suffer," he added.
The president said Tuesday he would not sign it unless stimulus checks were increased from $600 to $2,000. Expanded unemployment benefits for millions of Americans lapsed Saturday after Trump refused to sign the COVID-19 relief bill.
A request from House Democrats to pass a standalone bill sending $2,000 stimulus checks was blocked Thursday by House Republicans. House Speaker Nancy Pelosi said in a statement that the House would hold a recorded vote on the measure Monday.
Senate Majority Leader Mitch McConnell has largely been silent on the president's request to increase stimulus checks.
On "This Week," Karl asked Hogan "why aren't more Republicans standing up to (the president)?"
"I think more and more are and will," Hogan said. "And I can tell you, there's an awful lot of concern right now. I mean, Republicans were put in this position, a lot of them came to support this bill even though they didn't like everything that was in it, even though perhaps it didn't have all the things we needed in it."
"It doesn't solve all the problems. But it's something," he added. "And if the president wants to come up with more money to help more people, terrific. Let's sign this bill now so we can start getting our unemployment benefits out right away, and then quickly pass another bill."
Hogan also responded to Trump urging congressional Republicans to challenge the election results when Congress votes to certify them on Jan. 6.
"Joe Biden is the properly elected president of the United States, whether people like that result or not," Hogan said Sunday. "And he is the president-elect. He will be sworn in on January 20th. And on January 6th, which is coming up pretty soon, he will be certified by the Congress."
Earlier in the interview, Hogan told Karl that he felt Biden has been reaching out to Republicans, citing meetings the president-elect had with both Democratic and Republican governors.
"He seems to be listening to us and our concerns about the things that are important in our state as we go through this, you know, critical fight against the virus and the economic troubles we're going through," Hogan said. "So I'm hoping he's going to follow through on that."
As for Trump's role in the Republican Party after he leaves office, Hogan said things would be different after Inauguration Day.
"He certainly has an oversized voice in the party," he said. "It's going to be a lot different after January 20th, when he's not in the position to exert such influence as he does now."
"There's an awful lot of people that want to be the next Donald Trump but I'm going to be fighting to try to return our party to its roots," Hogan added. "And to become a bigger-tent party to reach out -- a more Reagan-esque party. More positive, hopeful visions for the future."