Republicans on Sunday expressed hope that President Obama's recent outreach to Congressional Republicans will lead to substantive negotiations, but cautioned that only time will tell whether it will.

"I think he's genuinely reaching out," Sen. Tom Coburn (R-Okla.) said of Obama on NBC News' "Meet The Press." "But you know, you've got a lot of scabs and sores on people, and it's going to take a while for that to heal."

"I hope that he's genuine," Rep. Cory Gardner (R-Colo.) said on the same program. "But I don't think we're going to be doing the Harlem Shake anytime soon together. I think that we can actually use this chance to see what's going to happen."

Obama is set to meet with Republican and Democratic leaders on Capitol Hill this week, as debate over the budget is set to heat up. Last week, Obama had dinner with some Senate Republicans, including Coburn, and lunched with House Budget Committee Chairman Paul Ryan (R-Wis.).

Sen. Ron Johnson (R-Wis.), one of the senators at last week's dinner, said on ABC News' "This Week With George Stephanopoulos" that he would "give the president the benefit of the doubt," and is hopeful his outreach will lead to substantive negotiations.

For his part, Ryan said the next few weeks will tell whether anything will come of Obama's outreach.

“The proof will be in the coming weeks as to whether or not it is a real sincere outreach to find common ground,” Ryan said on "Fox News Sunday."

Former Florida governor Jeb Bush (R) said that if Obama can cultivate a meaningful dialogue with Republicans, it could make a real difference in the conversation in Washington.

"I don't know the president's motivations," Bush said on CBS News' "Face The Nation." "I do know that if he reaches out and builds a dialogue where there's greater trust and there's a personal relationship, it matters. It's mattered for all presidents and it would matter for him."

Bush also reiterated a point he made last week, saying that new tax revenue increases -- which Republican leaders have opposed -- shouldn't be completely off the table in negotiations over the nation's deficit.

"I wouldn't say no, heck no, and that's it. What I would do is advocate policies that would create high growth because the revenue collected by government when you're growing at 3.5% instead of 1.5% is exponentially more," said Bush.

Sen. Rob Portman (R-Ohio) said the president's outreach is encouraging, but it's Obama's own party that needs convincing, when it comes to entitlement reform.

"What the president needs to do is reach out not just to Republicans but to Democrats, and to ensure that he gives them the political cover to do, frankly, what most of them know needs to be done," Portman said on "Face The Nation."

Democrats, for their part, called on their Republican colleagues to compromise. Rep. Chris Van Hollen (D-Md.), the ranking Democrat on the House Budget Committee, said Republicans need to drop their resistance to closing tax loopholes to increase revenue.

"More talk is good, but ultimately, we need everybody to come together and compromise around a balanced approach," Van Hollen said on "Face The Nation."

Sen. Tim Kaine (D-Va.) said on "Meet The Press": "We can ask the president to do more, but the only fix of Congress is Congress's to fix."