"It's just not that simple and easy," Ryan said on CBS's "Face the Nation."
"We, all Republicans, want to repeal and replace ObamaCare. ... Rather than sort of swinging for the fences and trying to take this entire law out with discretionary spending, I think there are more effective ways of achieving that goal."
Ryan said he would support delaying parts of the law's implementation, calling it a "better" strategy that also has support from some Democrats.
Conservative Republicans in the Senate are trying to rally support for their shutdown threat over the month of August.
To carry it out, senators like Mike Lee (R-Utah), Ted Cruz (R-Texas) and Marco Rubio (R-Fla.) would block any government funding bill that contains money for ObamaCare.
That move would force a stalemate as the clock ticks down to Sept. 30, when the current funding bill expires and a government shutdown would take effect.
The strategy has split congressional Republicans, with conservatives arguing it's the best way to finally thwart ObamaCare and skeptics saying the push would backfire and hurt Republicans.